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2,000 | Conformal invariance in two-dimensional percolation | math-ph | The immediate purpose of the paper was neither to review the basic
definitions of percolation theory nor to rehearse the general physical notions
of universality and renormalization (an important technique to be described in
Part Two). It was rather to describe as concretely as possible, although in
hypothetical form, ... | math |
2,001 | Gauge Symmetry and Integrable Models | math-ph | We establish the isomorphism between a nonlinear $\sigma$-model and the
abelian gauge theory on an arbitrary curved background, which allows us to
derive integrable models and the corresponding Lax representations from gauge
theoretical point of view. In our approach the spectral parameter is related to
the global degr... | math |
2,002 | Vortex Dynamics for the Ginzburg-Landau-Schrödinger Equation | math-ph | The initial value problem for the Ginzburg-Landau-Schr\"odinger equation is
examined in the $\epsilon \rightarrow 0$ limit under two main assumptions on
the initial data $\phi^\epsilon$. The first assumption is that $\phi^\epsilon$
exhibits $m$ distinct vortices of degree $\pm 1$; these are described as points
of conce... | math |
2,003 | On a $p$-Laplacian type of evolution system and applications to the Bean model in the type-II superconductivity theory | math-ph | We study the Cauchy problem for an $p$-Laplacian type of evolution system
${\mathbf H}_{t}+\g [ | \g {\mathbf H}|^{p-2} \g {\mathbf H}|]={\mathbf F}$.
This system governs the evolution of a magnetic field ${\bf H}$, where the
current displacement is neglected and the electrical resistivity is assumed to
be some power o... | math |
2,004 | Symmetry of the Schrödinger equation with variable potential | math-ph | We study symmetry properties of the Schr\"odinger equation with the potential
as a new dependent variable, i.e., the transformations which do not change the
form of the class of equations. We also consider systems of the Schr\"odinger
equations with certain conditions on the potential. In addition we investigate
symmet... | math |
2,005 | Stochastic cohomology of the frame bundle of the loop space | math-ph | We study the differential forms over the frame bundle of the based loop
space. They are stochastics in the sense that we put over this frame bundle a
probability measure. In order to understand the curvatures phenomena which
appear when we look at the Lie bracket of two horizontal vector fields, we
impose some regulari... | math |
2,006 | The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra | math-ph | We investigate closed ideals in the Grassmann algebra serving as bases of
Lie-invariant geometric objects studied before by E. Cartan. Especially, the E.
Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be
treated in the frame work of the Wahlquist Estabrook prolongation structures on
jet-man... | math |
2,007 | Lie symmetries of Einstein's vacuum equations in N dimensions | math-ph | We investigate Lie symmetries of Einstein's vacuum equations in N dimensions,
with a cosmological term. For this purpose, we first write down the second
prolongation of the symmetry generating vector fields, and compute its action
on Einstein's equations. Instead of setting to zero the coefficients of all
independent p... | math |
2,008 | On the Moyal quantized BKP type hierarchies | math-ph | Quantization of BKP type equations are done through the Moyal bracket and the
formalism of pseudo-differential operators. It is shown that a variant of the
dressing operator can also be constructed for such quantized systems. | math |
2,009 | Finding Exact Values For Infinite Sums | math-ph | This paper offers a solution method that allows one to find exact values for
a large class of convergent series of rational terms. Sums of this form arise
often in problems dealing with Quantum Field Theory. | math |
2,010 | Quantum Analysis and Nonequilibrium Response | math-ph | The quantum derivatives of $e^{-A}, A^{-1}$ and $\log A$, which play a basic
role in quantum statistical physics, are derived and their convergence is
proven for an unbounded positive operator $A$ in a Hilbert space. Using the
quantum analysis based on these quantum derivatives, a basic equation for the
entropy operato... | math |
2,011 | The Fuzzy Supersphere | math-ph | We introduce the fuzzy supersphere as sequence of finite-dimensional,
noncommutative $Z_{2}$-graded algebras tending in a suitable limit to a dense
subalgebra of the $Z_{2}$-graded algebra of ${\cal H}^{\infty}$-functions on
the $(2| 2)$-dimensional supersphere. Noncommutative analogues of the body map
(to the (fuzzy) ... | math |
2,012 | Quantum Mechanics on the h-deformed Quantum Plane | math-ph | We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami
operator on the extended $h$-deformed quantum plane and solve the Schr\"odinger
equations explicitly for some physical systems on the quantum plane. In the
commutative limit the behaviour of a quantum particle on the quantum plane
becomes that o... | math |
2,013 | Lie symmetries, Kac-Moody-Virasoro algebras and integrability of certain (2+1)-dimensional nonlinear evolution equations | math-ph | In this paper we study Lie symmetries, Kac-Moody-Virasoro algebras,
similarity reductions and particular solutions of two different recently
introduced (2+1)-dimensional nonlinear evolution equations, namely (i)
(2+1)-dimensional breaking soliton equation and (ii) (2+1)-dimensional
nonlinear Schr\"odinger type equation... | math |
2,014 | A method for obtaining Darboux transformations | math-ph | In this paper we give a method to obtain Darboux transformations (DTs) of
integrable equations. As an example we give a DT of the dispersive water wave
equation. Using the Miura map, we also obtain the DT of the Jaulent-Miodek
equation. \end{abstract} | math |
2,015 | Kinematical symmetries of 3D incompressible flows | math-ph | The motion of an incompressible fluid in Lagrangian coordinates involves
infinitely many symmetries generated by the left Lie algebra of group of volume
preserving diffeomorphisms of the three dimensional domain occupied by the
fluid. Utilizing a 1+3-dimensional Hamiltonian setting an explicit realization
of this symme... | math |
2,016 | A time-extended Hamiltonian formalism | math-ph | A Poisson structure on the time-extended space R x M is shown to be
appropriate for a Hamiltonian formalism in which time is no more a privileged
variable and no a priori geometry is assumed on the space M of motions.
Possible geometries induced on the spatial domain M are investigated. An
abstract representation space... | math |
2,017 | "Tunneling" Amplitudes of a Massless Quantum Field | math-ph | We propose a method for the approximate computation of the Green function of
a scalar massless field subjected to potential barriers of given size and shape
in spacetime. The potential of the barriers has the form
V(phi)=xi(phi^2-phi_0^2)^2; xi is very large and phi_0 very close to zero, the
product (xi phi_0^2) being ... | math |
2,018 | Deformation in Phase Space | math-ph | We review several procedures of quantization formulated in the framework of
(classical) phase space M. These quantization methods consider Quantum
Mechanics as a "deformation" of Classical Mechanics by means of the
"transformation" of the commutative algebra of smooth functions on M in a new
non-commutative algebra. Th... | math |
2,019 | Long time semiclassical approximation of quantum flows: a proof of the Ehrenfest time | math-ph | Let ${\cal H}(x,\xi)$ be a holomorphic Hamiltonian of quadratic growth on $
R^{2n}$, $b$ a holomorphic exponentially localized observable, $H$, $B$ the
corresponding operators on $L^2(R^n)$ generated by Weyl quantization, and
$U(t)=\exp{iHt/\hbar}$. It is proved that the $L^2$ norm of the difference
between the Heisenb... | math |
2,020 | Dynamic Connections in Analytical Mechanics | math-ph | It is shown that any dynamic equation on a configuration bundle $Q\to R$ of
non-relativistic time-dependent mechanics is associated with connections on the
affine jet bundle $J^1Q\to Q$ and on the tangent bundle $TQ\to Q$. As a
consequence, any non-relativistic dynamic equation can be seen as a geodesic
equation with r... | math |
2,021 | Generating Functions for Multi-j-Symbols | math-ph | A formula is derived that provides generating functions for any
multi-j-symbol, such as the 3-j-symbol, the 6-j-symbol, the 9-j-symbol, etc.
The result is completely determined by geometrical objects (loops and curves)
in the graph of the the multi-j-symbol. A geometric-combinatorical
interpretation for multi-j-symbols... | math |
2,022 | Continuum Limits for Critical Percolation and Other Stochastic Geometric Models | math-ph | The talk presented at ICMP 97 focused on the scaling limits of critical
percolation models, and some other systems whose salient features can be
described by collections of random lines. In the scaling limit we keep track of
features seen on the macroscopic scale, in situations where the short--distance
scale at which ... | math |
2,023 | The discrete spectrum in the singular Friedrichs model | math-ph | A typical result of the paper is the following. Let $H_\gamma=H_0 +\gamma V$
where $H_0$ is multiplication by $|x|^{2l}$ and $V$ is an integral operator
with kernel $\cos< x,y\rang le$ in the space $L_2(R^d)$. If $l=d/2+ 2k$ for
some $k= 0,1,...$, then the operator $H_\gamma$ has infinite number of negative
eigenvalues... | math |
2,024 | Dual Killing-Yano symmetry and multipole moments in electromagnetism and mechanics of continua | math-ph | In this work we introduce the Killing-Yano symmetry on the phase space and we
investigate the symplectic structure on the space of Killing-Yano tensors. We
perform the detailed analyze of the $n$-dimensional flat space and the
Riemaniann manifolds with constant scalar curvature. We investigate the form of
some multipol... | math |
2,025 | A sharp bound for an eigenvalue moment of the one-dimensional Schroedinger operator | math-ph | We give a proof of the Lieb-Thirring inequality in the critical case $d=1$,
$\gamma= 1/2$, which yields the best possible constant. | math |
2,026 | Quantum Transport in Molecular Rings and Chains | math-ph | We study charge transport driven by deformations in molecular rings and
chains. Level crossings and the associated Longuet-Higgins phase play a central
role in this theory. In molecular rings a vanishing cycle of shears pinching a
gap closure leads, generically, to diverging charge transport around the ring.
We call su... | math |
2,027 | Vlasov Equation In Magnetic Field | math-ph | The linearized Vlasov equation for a plasma system in a uniform magnetic
field and the corresponding linear Vlasov operator are studied. The spectrum
and the corresponding eigenfunctions of the Vlasov operator are found. The
spectrum of this operator consists of two parts: one is continuous and real;
the other is discr... | math |
2,028 | Classification of seven-vertex solutions of the coloured Yang-Baxter equation | math-ph | In this paper all seven-vertex type solutions of the coloured Yang-Baxter
equation dependent on spectral as well as coloured parameters are given. It is
proved that they are composed of five groups of basic solutions, two groups of
their degenerate forms up to five solution transformations. Moreover, all
solutions can ... | math |
2,029 | A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition | math-ph | The Gutzwiller semiclassical trace formula links the eigenvalues of the
Scrodinger operator ^H with the closed orbits of the corresponding classical
mechanical system, associated with the Hamiltonian H, when the Planck constant
is small ("semiclassical regime"). Gutzwiller gave a heuristic proof, using the
Feynman inte... | math |
2,030 | A Mourre estimate for a Schroedinger operator on a binary tree | math-ph | Let G be a binary tree with vertices V and let H be a Schroedinger operator
acting on l^{2}(V). A decomposition of the space l^{2}(V) into invariant
subspaces is exhibited yielding a conjugate operator A, for use in the Mourre
estimate. We show that for potentials q satisfying a first order difference
decay condition, ... | math |
2,031 | Classical Geometric Interaction- picture-like Description | math-ph | In order to get the classical analogue of quantum interaction picture in
classical symplectic geometric description, the space of solutions of free
equations of motion is suggested to replace the phase space in $T^{*}Q$
description or the space of motions in usual classical symplectic geometric
description. The way to ... | math |
2,032 | Volume preserving multidimensional integrable systems and Nambu-Poisson Geometry | math-ph | In this paper we study generalized classes of volume preserving
multidimensional integrable systems via Nambu-Poisson mechanics. These
integrable systems belong to the same class of dispersionless KP type equation.
Hence they bear a close resemblance to the self dual Einstein equation.
Recently Takasaki-Takebe provided... | math |
2,033 | Exponential Estimates in Adiabatic Quantum Evolution | math-ph | We review recent results concerning the exponential behaviour of transition
probabilities across a gap in the adiabatic limit of the time-dependent
Schr\"odinger equation. They range from an exponential estimate in quite
general situations to asymptotic Landau-Zener type formulae for finite
dimensional systems, or syst... | math |
2,034 | A (2+1)-dimensional integrable spin model(the M-XXII equation) and Differential geometry of curves/surfaces | math-ph | Using the differential geometry of curves and surfaces the Lakshmanan
equivalent counterpart of the M-XXII equation is found ... . | math |
2,035 | A solvable many-body problem in the plane | math-ph | A solvable many-body problem in the plane is exhibited. It is characterized
by rotation-invariant Newtonian (``acceleration equal force'') equations of
motion, featuring one-body (``external'') and pair (``interparticle'') forces.
The former depend quadratically on the velocity, and nonlinearly on the
coordinate, of th... | math |
2,036 | Matrix exponential via Clifford algebras | math-ph | We use isomorphism $\varphi$ between matrix algebras and simple orthogonal
Clifford algebras $\cl(Q)$ to compute matrix exponential ${e}^{A}$ of a real,
complex, and quaternionic matrix A. The isomorphic image $p=\varphi(A)$ in
$\cl(Q),$ where the quadratic form $Q$ has a suitable signature $(p,q),$ is
exponentiated mo... | math |
2,037 | A New Look at the Multidimensional Inverse Scattering Problem | math-ph | As a prototype of an evolution equation we consider the Schr\"odinger
equation i (d/dt) \Psi(t) = H \Psi(t), H = H_0 + V(x) for the Hilbert space
valued function \Psi(.) which describes the state of the system at time t in
space dimension at least 2. The kinetic energy operator H_0 may be propotional
to the Laplacian (... | math |
2,038 | The modified Bargmann-Wigner formalism: The Higher Spins | math-ph | In the old articles of Ogievetskii and Polubarinov, Kalb and Ramond the
notoph concept, the longitudinal field originated from the antisymmetric tensor
(AST), has been proposed. In our work we analyze the theory of the AST field of
the second rank from the viewpoint of the normalization problem. We obtain
4-potentials ... | math |
2,039 | Generalization of Integrality Condition of Prequantization to Phase Space with Boundaries | math-ph | The Weil's integrality condition of prequantization line bundle is
generalized to phase space with boundaries. The proofs of both necessity and
sufficiency are given. It is pointed out via the method of topological current
that Weil's integrality condition is closely connected with the summation of
index of isolated si... | math |
2,040 | Twist Positivity | math-ph | We identify a positivity property for partition functions in quantum systems
with a unitary symmetry group, and we call this "twist positivity." The
existence of Feynman-Kac measures and the existence of zero-mass limits are
both related to this property. Twist positivity arises from the occurrence of
complex conjugate... | math |
2,041 | Geometric Quantization of free fields in space of motions | math-ph | Via K$\ddot{a}$hker polarization we geometrically quantize free fields in the
spaces of motions, namely the space of solutions of equations of motion. We
obtain the correct results just as that given by the canonical quantization.
Since we follow the method of covariant symplectic current proposed by
Crnkovic, Witten a... | math |
2,042 | On complex structures in physics | math-ph | Complex numbers enter fundamental physics in at least two rather distinct
ways. They are needed in quantum theories to make linear differential operators
into Hermitian observables. Complex structures appear also, through Hodge
duality, in vector and spinor spaces associated with space-time. This paper
reviews some of ... | math |
2,043 | Noncommutative geometry and a class of completely integrable models | math-ph | We introduce a Hodge operator in a framework of noncommutative geometry. The
complete integrability of 2-dimensional classical harmonic maps into groups
(sigma-models or principal chiral models) is then extended to a class of
'noncommutative' harmonic maps into matrix algebras. | math |
2,044 | About a resolvent formula | math-ph | A resolvent formula, originally presented by Karner in his habilitation, is
discussed. First the formula is considered abstractly and then it is
demonstrated on an explicit example -- the so called simplified Fermi
accelerator. | math |
2,045 | Application of chaos degree to some dynamical systems | math-ph | Chaos degree defined through two complexities in information dynamics is
applied to some deterministic dynamical models. It is shown that this degree
well describes the chaostic feature of the models. | math |
2,046 | Interface states of quantum spin systems | math-ph | We review recent results as well as ongoing work and open problems concerning
interface states in quantum spin systems at zero and finite temperature. | math |
2,047 | Transfer matrices, non-Hermitian Hamiltonians and Resolvents: some spectral identities | math-ph | I consider the N-step transfer matrix T for a general block Hamiltonian, with
eigenvalue equation
L_n \psi_{n+1} + H_n \psi_n + L_{n-1}^\dagger \psi_{n-1} = E \psi_n
where H_n and L_n are matrices, and provide its explicit representation in
terms of blocks of the resolvent of the Hamiltonian matrix for the system o... | math |
2,048 | Identities involving elementary symmetric functions | math-ph | A systematic procedure for generating certain identities involving elementary
symmetric functions is proposed. These identities, as particular cases, lead to
new identities for binomial and q-binomial coefficients. | math |
2,049 | Gauge invariance of the Chern-Simons action in noncommutative geometry | math-ph | In complete analogy with the classical case, we define the Chern-Simons
action functional in noncommutative geometry and study its properties under
gauge transformations. As usual, the latter are related to the connectedness of
the group of gauge transformations. We establish this result by making use of
the coupling b... | math |
2,050 | The representation theory of decoherence functionals in history quantum theories | math-ph | In the first part of this paper the general perspective of history quantum
theories is reviewed. History quantum theories provide a conceptual and
mathematical framework for formulating quantum theories without a globally
defined Hamiltonian time evolution and for introducing the concept of space
time event into quantu... | math |
2,051 | Resonances In a Box | math-ph | We investigate a numerical method for studying resonances in quantum
mechanics. We prove rigorously that this method yields accurate approximations
to resonance energies and widths for shape resonances in the semiclassical
limit. | math |
2,052 | Remarks on random evolutions in Hamiltonian representation | math-ph | telegrapher's equations and some random walks of Poisson type are shown to
fit into the framework of the Hamiltonian formalism after an appropriate
time-dependent rescaling of the basic variables has been made. | math |
2,053 | On asymptotic nonlocal symmetry of nonlinear Schrödinger equations | math-ph | A concept of asymptotic symmetry is introduced which is based on a definition
of symmetry as a reducibility property relative to a corresponding invariant
ansatz. It is shown that the nonlocal Lorentz invariance of the free-particle
Schr\"odinger equation, discovered by Fushchych and Segeda in 1977, can be
extended to ... | math |
2,054 | Solving simultaneously Dirac and Ricatti equations | math-ph | We analyse the behaviour of the Dirac equation in $d=1+1$ with Lorentz scalar
potential. As the system is known to provide a physical realization of
supersymmetric quantum mechanics, we take advantage of the factorization method
in order to enlarge the restricted class of solvable problems. To be precise,
it suffices t... | math |
2,055 | Symmetry group analysis of relativistic heat conducting fluids | math-ph | The Lie symmetry group for 1+1 dimensional relativistic heat-conducting fluid
is calculated for two different theories, Eckart and Israel-Stewart and a
comparison between the group-invariant solutions has been made. Both fluids
were founded to be physical acceptable in the sense that during the evolution
of the fluid t... | math |
2,056 | The gauge freedoms of enlarged Helmholtz theorem and the Neumann --- Debye potentials; their manifestation in the multipole expansion of conserved current | math-ph | We discuss gauge freedom within the scope of the enlarged Helmholtz theorem
and Neumann-Debye decomposition and then demonstrate its realization for the
multipole expansion of a electromagnetic current with distinguished toroid
moment family. The exact solution to the latter problem was obtained in 1974,
but answers to... | math |
2,057 | Discrete spectrum for n-cell potentials | math-ph | We study the scattering problem, the Sturm-Liouville problem and the spectral
problem with periodic or skew-periodic boundary conditions for the
one-dimensional Schr\"odinger equation with an $n$-cell (finite periodic)
potential. We give explicit upper and lower bounds for the distribution
functions of discrete spectru... | math |
2,058 | Higher-Order Quantization on a Lie Group | math-ph | In this paper we are mainly concerned with the study of polarizations (in
general of higher-order type) on a connected Lie group with a U(1)-principal
bundle structure. The representation technique used here is formulated on the
basis of a group quantization formalism previously introduced which generalizes
the Kostant... | math |
2,059 | Asymptotic distribution of zeros of polynomials satisfying difference equations | math-ph | We propose a way to find the asymptotic distribution of zeros of orthogonal
polynomials p_n(x) satisfying a difference equation of the form
B(x)p_n(x+\delta)-C(x,n)p_n(x)+D(x)p_n(x-\delta)=0. We calculate the asymptotic
distribution of zeros and asymptotics of extreme zeros of the Meixner and
Meixner-Pollaczek polynomi... | math |
2,060 | Modelling of Phase Separation in Alloys with Coherent Elastic Misfit | math-ph | Elastic interactions arising from a difference of lattice spacing between two
coherent phases can have a strong influence on the phase separation
(coarsening) of alloys. If the elastic moduli are different in the two phases,
the elastic interactions may accelerate, slow down or even stop the phase
separation process. I... | math |
2,061 | Irreducible bases in icosahedral group space | math-ph | The irreducible bases in the icosahedral group space are calculated
explicitly by reducing the regular representation. The symmetry adapted bases
of the system with {\bf I} or {\bf I}$_{h}$ symmetry can be calculated easily
and generally by applying those irreducible bases to wavefunctions of the
system, if they are no... | math |
2,062 | Irreducible bases and correlations of spin states for double point groups | math-ph | In terms of the irreducible bases of the group space of the octahedral double
group {\bf O'}, an analytic formula is obtained to combine the spin states
$|j,\mu \rangle$ into the symmetrical adapted bases, belonging to a given row
of a given irreducible representation of {\bf O'}. This method is effective for
all doubl... | math |
2,063 | On Symmetric Operators in Noncommutative Geometry | math-ph | In Noncommutative Geometry, as in quantum theory, classically real variables
are assumed to correspond to self-adjoint operators. We consider the relaxation
of the requirement of self-adjointness to mere symmetry for operators $X_i$
which encode space-time information. | math |
2,064 | Instability of a Pseudo-Relativistic Model of Matter with Self-Generated Magnetic Field | math-ph | For a pseudo-relativistic model of matter, based on the no-pair Hamiltonian,
we prove that the inclusion of the interaction with the self-generated magnetic
field leads to instability for all positive values of the fine structure
constant. This is true no matter whether this interaction is accounted for by
the Breit po... | math |
2,065 | Correlations of spin states for icosahedral double group | math-ph | The irreducible bases of the group space of the icosahedral double groups
{\bf I'} and {\bf I$_{h}'$} are calculated explicitly. Applying those bases on
the spin states $|j,\mu>$, we present a simple formula to combine the spin
states into the symmetrical adapted bases, belonging to a given row of a given
irreducible r... | math |
2,066 | Physico--Mathematical Interactions: The Chern--Simons Story | math-ph | The essential role played by Chern--Simons terms in a variety of physical
models provides yet another illustration of the unexpected but profound
interactions between the two disciplines. | math |
2,067 | Helicity invariants in 3D : kinematical aspects | math-ph | Exact, degenerate two-forms on time-extended space R X M which are invariant
under the unsteady, incompressible fluid motion on 3D region M are introduced.
The equivalence class up to exact one-forms of each potential one-form is
splitted by the velocity field. The components of this splitting corresponds to
Lagrangian... | math |
2,068 | h analogue of Newton's binomial formula | math-ph | In this letter, the $h$--analogue of Newton's binomial formula is obtained in
the $h$--deformed quantum plane which does not have any $q$--analogue. For
$h=0$, this is just the usual one as it should be. Furthermore, the binomial
coefficients reduce to $\frac{n!}{(n-k)!}$ for $h=1$. \\ Some properties of the
$h$--binom... | math |
2,069 | Compatibility of distortion fields caused by topological defects in 2D latties | math-ph | Topological defects in crystalline lattices are considered. In relation to
physical realizability of such defects, criteria for geometric compatibility of
the lattice distortions are formulated. For 2D lattices it is shown that the
answer to the question of existence of distortion fields which are both
geometrically co... | math |
2,070 | Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings | math-ph | We formulate an adiabatic theorem adapted to models that present an
instantaneous eigenvalue experiencing an infinite number of crossings with the
rest of the spectrum. We give an upper bound on the leading correction terms
with respect to the adiabatic limit. The result requires only differentiability
of the considere... | math |
2,071 | Semiclassical Dynamics with Exponentially Small Error Estimates | math-ph | We construct approximate solutions to the time--dependent Schr\"odinger
equation $i \hbar (\partial \psi)/(\partial t) = - (\hbar^2)/2 \Delta \psi + V
\psi$ for small values of $\hbar$. If $V$ satisfies appropriate analyticity and
growth hypotheses and $|t|\le T$, these solutions agree with exact solutions up
to errors... | math |
2,072 | The form factors in the finite volume | math-ph | The form factors of integrable models in finite volume are studied. We
construct the explicite representations for the form factors in terms of
determinants. | math |
2,073 | (q,h)-analogue of Newton's binomial formula | math-ph | In this letter, the (q,h)-analogue of Newton's binomial formula is obtained
in the (q,h)-deformed quantum plane which reduces for h=0 to the q-analogue.
For (q=1,h=0), this is just the usual one as it should be. Moreover, the
h-analogue is recovered for q=1. Some properties of the (q,h)-binomial
coefficients are also g... | math |
2,074 | Finslerian N-spinor algebra | math-ph | New mathematical objects called Finslerian N-spinors are discussed. The
Finslerian N-spinor algebra is developed. It is found that Finslerian N-spinors
are associated with an N^2-dimensional flat Finslerian space. A generalization
of the epimorphism SL(2,C) --> SO^\uparrow(1,3) to a case of the group SL(N,C)
is constru... | math |
2,075 | The Full Laplace-Beltrami operator on U(N) and SU(N) | math-ph | The Laplacian on the Lie groups U(N) and SU(N) is given in a parametrized
edition for practical purposes. The radial part is often seen in work on
lattice gauge theory, but here is derived also the off-diagonal part which in
SU(3) and U(3) is expressed via the well known Gell-Mann matrices but with a
more easily memori... | math |
2,076 | Classical Mechanics and geometric Quantization on an Infinite Dimensional Disc and Grassmannian | math-ph | We discuss the classical mechanics on the Grassmannian and the Disc modeled
on the ideal L^(2,\infty)(H). We apply methods of geometric quantization to
these systems. Their relation to a flat symplectic space is also discussed. | math |
2,077 | On SL(3,C)-covariant spinor equation and generalized Duffin-Kemmer algebra | math-ph | The SL(3,C)-covariant 9-dimensional equation for a free 3-spinor particle is
transformed into the Dirac-like form (p_A\delta^A - M)\Psi=0. However, the
corresponding \delta matrices do not satisfy the Dirac algebra. It is shown
that \delta^A lead to a Finslerian generalization of the Duffin-Kemmer algebra.
The Appendix... | math |
2,078 | Multi-time correlations in quantized toral automorphisms | math-ph | The long time asymptotics of multi-time correlation functions of relaxing
quantum mechanical systems can be conveniently studied by means of
free-products of suitable C*-algebras and of states on these free products
given by multiple temporal averages. In this paper, we study the distribution
law of fluctuations of tem... | math |
2,079 | Contact symmetry of time-dependent Schrödinger equation for a two-particle system: symmetry classification of two-body central potentials | math-ph | Symmetry classification of two-body central potentials in a two-particle
Schr\"{o}dinger equation in terms of contact transformations of the equation
has been investigated. Explicit calculation has shown that they are of the same
four different classes as for the point transformations. Thus in this problem
contact tran... | math |
2,080 | Dynamical correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions | math-ph | We study the time and temperature dependent correlation functions for an
impenetrable Bose gas with Neumann or Dirichlet boundary conditions $\langle
\psi(x_1,0)\psi^\dagger(x_2,t)\rangle _{\pm,T}$. We derive the Fredholm
determinant formulae for the correlation functions, by means of the Bethe
Ansatz. For the special ... | math |
2,081 | Existence of the Solution for the 't Hooft-Polyakov Monopole | math-ph | In this paper we give a mathematical proof of the existence of the time
independent and spherically symmetric solution to the 't Hooft-Polyakov model
of magnetic monopole by using 2D-shooting method. | math |
2,082 | Instability and Chaos in Spatially Homogeneous Field Theories | math-ph | Spatially homogeneous field theories are studied in the framework of
dynamical system theory. In particular we consider a model of inflationary
cosmology and a Yang-Mills-Higgs system. We discuss also the role of quantum
chaos and its application to field theories. | math |
2,083 | Periodic instantons and the loop group | math-ph | We construct a large class of periodic instantons. Conjecturally we produce
all periodic instantons. This confirms a conjecture of Garland and Murray that
relates periodic instantons to orbits of the loop group acting on an extension
of its Lie algebra. | math |
2,084 | Generalized functions for quantum fields obeying quadratic exchange relations | math-ph | The axiomatic formulation of quantum field theory (QFT) of the 1950's in
terms of fields defined as operator valued Schwartz distributions is
re-examined in the light of subsequent developments. These include, on the
physical side, the construction of a wealth of (2-dimensional) soluble QFT
models with quadratic exchan... | math |
2,085 | Drinfel'd Twists and Functional Bethe Ansatz | math-ph | Using Functional Bethe Ansatz technique, factorizing Drinfel'd Twists for any
finite dimensional irreducible representations of the Yangian Y(sl(2)) are
constructed. | math |
2,086 | Kink-like Configurations of Interacting Scalar, Electromagnetic, and Gravitational Fields | math-ph | We have obtained exact kink-like static plane-symmetric solutions to the
self-consistent system of electromagnetic, scalar, and gravitational field
equations. It was shown that under certain choice of the interaction Lagrangian
the solutions are regular and have localized energy. The linearized instability
of correspon... | math |
2,087 | Clifford Periodicity from Finite Groups | math-ph | We deduce the periodicity 8 for the type of $Pin$ and $Spin$ representations
of the orthogonal groups $O(n)$ from simple combinatorial properties of the
finite Clifford groups generated by the gamma matrices. We also include the
case of arbitrary signature $O(p,q)$. The changes in the type of representation
can be seen... | math |
2,088 | Mass Generation in the Large N nonlinear sigma-Model | math-ph | We study the infrared behaviour of the two-dimensional Euclidean O(N)
nonlinear sigma-Model with a suitable ultraviolet cutoff. It is proven that for
a sufficiently large (but finite!) number N of field components the model is
massive and thus has exponentially decaying correlation functions. We use a
representation of... | math |
2,089 | Constructive aspects of algebraic euclidean field theory | math-ph | This paper is concerned with constructive and structural aspects of euclidean
field theory. We present a C*-algebraic approach to lattice field theory.
Concepts like block spin transformations, action, effective action, and
continuum limits are generalized and reformulated within the C*-algebraic
setup. Our approach al... | math |
2,090 | Constructive Renormalization Theory | math-ph | These notes are the second part of a common course on Renormalization Theory
given with Professor P. da Veiga at X Jorge Andre Swieca Summer School, Aguas
de Lindoia, Brazil, February 7-12, 1999. I emphasize the rigorous
non-perturbative or constructive aspects of the theory. The usual formalism for
the renormalization... | math |
2,091 | Deduction of the law of motion of the charges from Maxwell equations | math-ph | By exploiting suitably a fundamental theorem by Hilbert, we show that the
equation of motion of the electric charges is a consequence of Maxwell field
equations. | math |
2,092 | Construction of Kink Sectors for Two-Dimensional Quantum Field Theory Models. An Algebraic Approach | math-ph | Several two-dimensional quantum field theory models have more than one vacuum
state. Familiar examples are the Sine-Gordon and the $\phi^4_2$-model. It is
known that in these models there are also states, called kink states, which
interpolate different vacua. A general construction scheme for kink states in
the framewo... | math |
2,093 | On the Product of Real Spectral Triples | math-ph | The product of two real spectral triples {A1,H1,D1,J1,gamma1} and
{A2,H2,D2,J2(,gamma2)}, the first of which is necessarily even, was defined by
A.Connes as {A,H,D,J(,gamma)} given by A=A1 x A2,H=H1 x H2, D=D1 x I2 + gamma1
x D2, J=J1 x J2 and by, in the even-even case, gamma=gamma1 x gamma2.
Generically it is assumed ... | math |
2,094 | Random Operators and Crossed Products | math-ph | This article is concerned with crossed products and their applications to
random operators. We study the von Neumann algebra of a dynamical system using
the underlying Hilbert algebra structure. This gives a particularly easy way to
introduce a trace on this von Neumann algebra. We review several formulas for
this trac... | math |
2,095 | Stretched Exponential Relaxation in the Biased Random Voter Model | math-ph | We study the relaxation properties of the voter model with i.i.d. random
bias. We prove under mild condions that the disorder-averaged relaxation of
this biased random voter model is faster than a stretched exponential with
exponent $d/(d+\alpha)$, where $0<\alpha\le 2$ depends on the transition rates
of the non-biased... | math |
2,096 | Goldstone Boson Normal Coordinates in Interacting Bose Gases | math-ph | For the phenomenon of Bose-Einstein condensation we construct the canonical
pair of field operators of the Goldstone Bosons explicitly as fluctuation
operators in the ground state. We consider the imperfect Bose gas as well as
the weakly interacting Bose gas. We prove that a canonical pair of fluctuation
operators is a... | math |
2,097 | Mathematical Structure of Magnons in Quantum Ferromagnets | math-ph | We provide the mathematical structure and a simple, transparent and rigorous
derivation of the magnons as elementary quasi-particle excitations at low
temperatures and in the infinite spin limit for a large class of Heisenberg
ferromagnets. The magnon canonical variables are obtained as fluctuation
operators in the inf... | math |
2,098 | Division of Differential operators, intertwine relations and Darboux Transformations | math-ph | The problem of a differential operator left- and right division is solved in
terms of generalized Bell polinomials for nonabelian differential unitary ring.
The definition of the polinomials is made by means of recurrent relations. The
expresions of classic Bell polinomils via generalized one is given. The
conditions o... | math |
2,099 | Tiling theory applied to the surface structure of icosahedral AlPdMn quasicrystals | math-ph | Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show
atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model
due to Elser which incorporates many experimental data. The model has
dodecahedral Bergman clusters within an icosahedral tiling T^*(2F) and is
projected from the 6D fa... | math |
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