instruction stringlengths 31 24.3k |
|---|
Given is a rectangular lattice (a=0.44 nm; b=0.34 nm), Fermi energy of $E_F = 6.4$eV and the energy/k dispersion along $k_a$ with $E(k)=E_0 - E_0 \cos(k\cdot a)$; $E_0 = 4$eV analogous in $k_b$ direction.
My issue is the following:
The wavevectors are defined through $k_a = \frac{\pi}{a}$ analogous for $k_b$. The energ... |
$$\require{cancel}$$
When encountering Dirac matrices, we immediately resort to using various elementary identities and simplify the expression for example:
$$(a)\ u(p)(\cancel{p}\gamma^\mu \cancel{p})\overline{u}(p')=u(p)((2p^\mu -\gamma^\mu \cancel{p})\cancel{p})\overline{u}(p')=u(p)(2p^\mu m -\gamma^\mu m^2)\overli... |
Since positive capacitor plate is always at a higher potential than negative, does this mean that we can only assume that current flows in a direction from positive to negative plate?
This, for example, would also explain the wrong and contradictory result I obtained from KVL in this question.
|
So hypothetically, you have a disc or ring. And on opposing edges of that disc/ring, there are two thrusters that given a set amount of Newtons of force (say 120 N) both in the counterclockwise direction.
Assume the axis is along the z dimension, so the direction of torque along that axis of rotation would be in the po... |
While the higher dimensional generalization of the angular momentum operator from $\vec L = \vec r\times\vec p$ in 3D to
\begin{align}
L_{ij} &= r_i p_j - r_j p_i
\end{align}
(and e.g. $L_z = L_{xy}$ in 3D) in $d$ dimensions is pretty straightforward, and it's square is then
$$L_d^2 := \frac12 \sum_{i,j=1}^d (L_{ij})... |
I am reading Griffith's textbook on particle physics about the $u+\bar d\rightarrow u+\bar d$ scattering for QCD. On page 285, it says there is only one possible channel ($t$-channel):
Why there are no other channels? If we have $u+ u\rightarrow u+u$ scattering, then $s$-channel is possible. Why is that the case? Als... |
A common type of experiment to demonstrate the greenhouse effect is essentially to direct heat lamps at the bottom of two closed jars, one with regular air in it, and one with a higher concentration of $\rm CO_2$. The jar with more $\rm CO_2$ in it heats to a higher temperature, and this is attributed to its infrared-a... |
Is it possible to write the relative angular momentum of three particles as a vector product of single position vector and single position momentum? I think that relative angular momentum can be defined as total angular momentum minus centre of mass angular momentum. To simplify let's assume equal masses. For instance ... |
The ionization is often defined as:
The energy needed to remove one or more electrons from a neutral atom to form a positively charged ion.
But what is meant by removed?
Suppose we have an infinitely large closed system with no content except a single atom (g). Now the ionisation energy can actually be as high as you... |
Two entangled particles are described (modeled) such that there may be a correlation between parts of the model. That is, measuring one of the pair provides information about the other. Why isn't this just a case of redundancy in the description/model, which, if reformulated to remove it would eliminate the correlati... |
The action of a system, say a scalar field is
$$ S = \int_{\mathcal{M}} {\rm d}^4 x ~ \mathcal{L}(\phi(x),\partial \phi(x)). $$
Now, if one does a variable transformation $x \to x'$, then
$$ S' = \int_{\mathcal{M}'} {\rm d}^4 x' ~ \mathcal{L}(\phi'(x'),\partial' \phi'(x')). $$
Then why isn't $S'$ guaranteed to be equal... |
How to prove that a drop of water in the weightlessness of space is round in shape theoretically? More specifically, how to prove that a drop of water in the weightlessness of space is round in shape with classical mechanics?
|
Im following Ncert textbook for physics and I was learning about Charge due to infinitely planar sheet. In this they say that the electric field due to the infinitely long planar sheet to be the same as the electric field enclosed within the gaussian surface
Title of subtopic: Field due to uniformly charged infinite p... |
In what frame of reference are the Euler and Lagrange time derivatives taken in?
I am beginning to study fluid mechanics, and there is a conceptual problem that I just can't shake. If you have a field of quantity $F(r,t)$, then computing the total time derivative would result in:
$$\frac{DF}{Dt} = \frac{\partial F}{\pa... |
So I have been tasked to determine at what precise length the classical calculations of the hydrogen atom break down.
I'll explain - the Coulomb interaction between the nucleus and the electron in the atom is a classical interaction, predicting that at some point the two will collide. Quantum mechanically this is not t... |
Background
Consider 1-D Ising model of n lattice points with periodic boundary condition,
$\beta H(\sigma_1,\sigma_2,...,\sigma_N) = -\sum_{i=1}^nk(\sigma_i\sigma_{i+1})-\sum_{i=1}^n\sigma_i$
$k=\beta J$ and $h=\beta B$ where $J$ is the coupling constant and $B$ is the applied magnetic field.
Partition function, $Z=\su... |
I am trying to understand what is bond dimension in tensor network more intuitively, by meaning of bond dimension I meant the tensor dimension that connects between tensors (in the example below the bond dimension will be the a's indices. .
I know that bond dimension related to the entanglement entropy with exponential... |
I am trying to work my way through this Wikipedia example and I was hoping somebody could help me answer a couple of questions.
If a 100 kg object is dragged for 10 m along a surface with the coefficient of friction μ = 0.5, the normal force is 981 N and the work done (required energy) is (work=force x distance) 981 ×... |
I have noticed that when discussing the resolution of a microscope or imaging system, the diffraction limit is often cited as the determining factor for what is resolvable or not. However, I am still unclear on how this impacts detection. For instance, in a reflection microscope, why does the point spread function (PSF... |
I understand roughly that Rayleigh scattering occurs when white light encounters particles smaller than the wavelength of visible light, and short wavelengths are preferentially scattered.
I'm wondering if this phenomenon is particular to electromagnetic radiation (e.g. if discrete energy quanta play an essential role)... |
In this video, after the piece with the camera separates from the main rotating machine, what causes it(the main rotating machine) to come off the attachments and fly off into the air? Is it due to less weight at one end due to the small piece with the camera flying off or is it due to some other reason?
Can anybody pl... |
Summary
I want to clarify how can I prove the fact that "the Noether charge generates the corresponding transformation" when the infinitesimal transformation of the fields contain the canonical momentum $\pi$.
Formulation
Let us consider the transformation of a set of scalar fields $\phi^i(x)$ on $D$-dimensional Minkow... |
Let $M$ be a Riemannian manifold and $\sigma$ the world function. The Van-Vleck-Morette determinant $D$ is defined by
$$D(x,x')=\det(-\sigma_{;\mu\nu{}'})$$
Regarding the semi-colon: In chapter $4.1$ of [K] it is claimed that it "denotes differentiation with
respect to the Levi-Civita connection", but in other referenc... |
I have a problem where I'm looking to find the following Hermitian operator $\hat{A}$ written in terms of the operators $\hat{a}^{\dagger}\hat{a}$, $\hat{a}^2$, $\hat{a}^{\dagger 2}$, $\hat{a}$, $\hat{a}^{\dagger}$, and $\mathbb{1}$ with coefficients $c_1$, $c_2$, $c_3$, and $c_4$ respectively as follows (${c_2,c_3}\in... |
If one tries to split a pair of quark and an anti quark, one ends up with two pairs, in the same way, when one tries to break a magnet in half, one end up in the same way with two magnets, so is this a coincidence?
|
For all matter to have been occupying the same point in space, this would violate the Pauli exclusion principle. Since fermions cannot occupy the same quantum state, the particles that are now fermions could not have been fermions at the point in the evolution of the universe where all particles occupied the same quant... |
I am considering a system with an ideal gas undergoing an adiabatic expansion. The initial volume is $V_0$ and final is $V$.
From this, How do I derive $\Delta S = Nk\ln(V/V_0)$ using fundamental equations of thermodynamics?
I know that $dQ=0$ as it is adiabatic, but im also a bit confused because doesnt that also mean... |
I'm struggling to understand heat conduction. If we have a finite heated rod where the temperature of one end is kept at a constant temperature, but the other end is perfectly insulated, what will the temperature distribution across the rod look like at a specific time? Will it decrease as you get to the insulated end ... |
I am following a propaedeutic course in quantum mechanics, and we did some basics of statistical mechanics deriving the Boltzmann equation for energy:
$$n_i=\frac{N}{Z}g_i e^\frac{-E_i}{kT}$$
where $n_i$ is the number of particles with $E_i$, $Z$ is the partition function, and $g_i$ is the multiplicity.
From that equat... |
I'm looking into Reynolds transport theorem (RTT) stated as:
$$ \frac{dB}{dt} = \frac{d}{dt} \int_{CV} b\rho dV+\int_{CS}b\rho(\underline{v}\cdot\underline{n}) dA$$
where B is defined as an extensive property and related to the intensive property b as $b = B/m$. I've seen how this equation is derived from the perspecti... |
There's a scenario where a car is moving between two points A and B in a way that it first goes 30m north and then 20m south in a time period of 10 seconds.
Now the speed of the car comes out to be 5 m/s while the velocity comes out to be 1m/s in the north direction.
So my doubt is that when I say that the speed of car... |
In introducing quantum field theory, the field solution to the Klein-Gordon equation is $$\phi(x^{\mu}) = \int \frac{a_{\bf{k}} e^{-i(k^{\mu}x_{\mu})} + a^{\dagger}_{\bf{k}} e^{i(k^{\mu}x_{\mu})}}{\sqrt{2\omega(2\pi)^3}} d\omega$$
The commutation relation is then $$[\phi(t, {\bf{x}}), \phi(t, {\bf{x^{'}}})] = 0$$
The v... |
I'm looking for the earliest references to the word spacetime (in the modern sense), in any language.
The first references would likely be in German, as Raum-zeit or Raumzeit.
Of course, H. Minkowski is credited as the originator of the idea. I found the following references to Minkowski's work in Pauli's Theory of Rel... |
Imagine to calculate the period of a pendulum using a software which takes his data from a cronometer that has an inerent instrumental uncertainty of 0.0025 s. In another discussion on this topic I found that the total uncertainty should be the sum in quadrature of both the instrumental and statistical error, so I woul... |
Many sources (DJ Griffiths, other answers on stack exchange) claim that the divergence of the vector field $\vec E=\frac{\hat r}{r^2}$, $\vec \nabla \cdot \vec E$ "blows up" at $\vec r=0$. But upon computation, we get an expression like $\frac{0}{r^2}$, which means it is 0 everwhere except origin, and at origin it is$\... |
When a system like this is placed in a uniform horizontal electric field with an initially slacked string, will that string become taut due to the electric field's action? Or does those spheres comes close to each other.
Once the charge flows from one sphere to another to balance the electric field inside the system,... |
Assume $c = 1$ for what follows.
For the general inhomogenous wave equation in one spatial dimension $$\left(\frac{\partial^2}{\partial t^2} - \frac{\partial^2}{\partial x^2}\right)\phi = v(x, t),$$ the article The Wave Equation with a Source gives (where we ignore the homogenous part of the solution, e.g. by setting i... |
I'm reading Greiner's good textbook "Thermodynamics and Statistical Mechanics" and I'm stuck on equation 6.22 on page 147 where he's counting the "number of ways" (aka countable permutations) that a microcanonical ensemble of N systems can be distributed to different locations of phase space.
See attached page 147 from... |
lets say we have some books resting on the floor.I am trying to find the maximum protuberance that the books can achieve.we see that the books on top of the initial book must have the center of mass in the edge of the initial book the formula for thee cneetr of mass is:
$$x_{cm} = \frac{mx_1+mx_2+...+mx_n}{m_1+m_2+...+... |
I have the following wave function in cylindrical coordinates,
$$\psi(q,\phi) = \frac{1}{\pi^(3/4)}\sqrt{\frac{n!}{(n+m)!}}q^me^\frac{-q^2}{2}L^m_n(q^2) $$
where $q$ is the nondimensionalized radial component and $\phi$ is the azimuthal angle.
So, this is the nondimensionalized wave function associated to Quantum Harmo... |
Let us imagine we have a book on a table. We want to push the table in such a way such that the book doesn't move with the table,instead it falls down vertically(assuming there is friction on the surface between the book and the table).This is a real life scenario which is possible. But i don't get the logic behind th... |
I'm learning about mechanical energy from Kleppner and Kolenkow (second edition), and in Chapter 5 (section 5.10), they introduce the notion of conservation of energy and connect it to the Einstein relation $E = mc^2$. Kleppner and Kolenkow give the following example:
In the 1930s, experimenters were able to measure n... |
So for integer spin, the way I understand it mathematically (in a classical limit), is that under a Lorentz transformation (i.e. change of coordinates), spin $n$ particles transform like rank $n$ covariant tensor fields. This makes wonderful sense to me because the induced representation of $SO^+(1,3)$ on $\bigotimes^n... |
If you are in a spaceship and you spin a sling with a rock in it, does the spaceship rotate in the opposite direction as the sling with the same angular, kinetic energy as the sling?
If the sling is released while spinning, and the rock flies off and hits the wall of the spaceship, does the spaceship obtain linear ve... |
I am not sure whether chemical equilibrium conditions are the same or different for the two scenarios below:
i. Closed rigid container of volume $V$ with uniform temperature $T$ and pressure $P$ filled with ideal gas of one kind with total particle count $N$. A partition divides the container into two components 1 and ... |
It is often stated that for lumped circuits the signal propagation can be considered instantaneous, so the the circuit parameters do not depend on space coordinates.
But how to actually derive this fact from Maxwell's equations?
First I would like to know how to derive the general space-dependent voltage and current ex... |
"Consider a hypothetical dense astronomical object with a mass of $2 × 10^{30}$ kg (about the mass of the sun), and a radius of $1.4 × 10^{14}$ m. Assuming you could stand on the surface of this object, if you fired a gun straight into the air, how high above the surface would the bullet go before turning around? The ... |
I am reading quantum mechanics and these two concepts are confusing me.
Griffths' QM book says "perturbation $H'\sim p^4$ is considered "spheric symmetric", so it commutes with $L^2$ and $L_z$." From my intuition, I understand potential $V(\mathbf r)=V(r)$ is spheric symmetric. However, why is operator "$p^4$" still s... |
The bonding state of H2 is |Ψ+>|0,0>. This makes sense because there is only 1 spatially symmetric state, in which the electrons experience an attractive exchange force. (|Ψ+> denotes spatial symmetry, |Ψ-> for spatial antisymmetry)
The antibonding orbital is formed by |Ψ+> and any of the three triplet spin states. How... |
I am interested in concentrating ions in a very small area, so the ion density of that region is elevated above normal levels.
What is the field of study, or term, that describes what I am talking about, and how have these been achieved?
(Edit: for clarity, I am not referring to nuclear fusion. I am looking for a field... |
I was asked in an interview to write the equation of a plane monochromatic wave. I wrote it as:
$$ E = E_0 \exp(i(k.x - wt)) $$
Now, they asked me to differentiate between this and light LASER.
Although I know the basics of both this seemed difficult as the main properties of LASER are directionality, monochromaticity,... |
Suppose an object is already rotating in a situation of no external forces such as gravity or friction. Is it possible or impossible for it's velocity (linear) to change by the shape of the object changing? For example if a piece of it broke off then collided and stuck back to the object in a different spot. It might b... |
I've always realised that areas in close proximity to the ocean experience moderate temperature changes. I don't understand how water moderates this temperature. I suspect that it has something to do with water's specific heat capacity in contrast to the specific heat capacity of land. How does this work?
|
Why is the top of the mountain cooler than the surface when the mountains are actually more closer to the sun and hence should be hotter?
|
My motivation for this question comes from the periodic table. There, the many-body ground state electronic configurations of certain atoms like boron or carbon can have a nonzero total orbital angular momentum. This can be interpreted as arising from the Pauli exclusion principle if one takes the approximate picture o... |
I want to calculate the phase diagram of $\rm Al$-$\rm Cu$ "by hand" in Python. The "regular" LIQ, FCC and BCC phases are all good (using the excess Gibbs energies from COST-507), where I find e.g. the LIQ-FCC boundary as such:
def AlCuLIQ(xAl, T):
pureTerm = xAl * AlG0LIQ(T) + (1 - xAl) * CuG0LIQ(T) # AlG0LIQ and ... |
The BCS wavefunction, with fixed number is written as
$$\left|\Psi_{BCS}(N)\right\rangle = \frac{1}{2\pi}\int_{0}^{2\pi} \mathrm{d}\phi\, e^{-iN\phi/2} \left|\Psi_{BCS}(\phi)\right\rangle \,\, ,$$
where:
$$\left|\Psi_{BCS}(\phi)\right\rangle = \left( |u_k| + e^{i\phi} |v_k| c_{k\uparrow}^{\dagger} c_{-k\downarrow}^{\da... |
When I search on this question online, I get conflicting answers. Most sites will tell you that the amplitude is not affected by the doppler shift, but in Einstein’s 1905 publication on special relativity (§7) he shows that the amplitude of an electromagnetic wave transforms with the same factor as the frequency. How c... |
I was trying to do this question and my original attempt went like this:
I see that my mistake was that I assumed that after friction is accounted for, the car will be pulled down into the same lane as if it were travelling at the given design speed (15.6464 m/s) AND that it would travel at the design speed.
So, my qu... |
I'm Korean highschool student and was writing a report about Euler beta function and string theory. And I can know find that Euler beta function is similar with the strong nuclear force equation. But I can't find the mathematical proof anywhere. Please explain me simply.
|
This question came about when I saw someone wearing clothing with a waveform on it. I wondered if it would be possible to reconstruct the original sound from the printed waveform.
I understand that a waveform is frequency over time. I have previously researched waveforms however most of the tutorials are about single t... |
$$
e^- + p \rightarrow \Delta^{++} + e^- + \pi^-
$$
Apparently this reaction is mediated by the EM force. My question is: how do you know it isn't the strong force?
Yes, all the particles have charge, suggesting it could be the EM force. But there are quarks involved too, so why is it not the strong force?
More... |
From the this reference, https://indico.in2p3.fr/event/1873/contributions/21752/attachments/17734/21715/delphes.pdf, it is stated that hadronic calorimeters are made up of heavy materials.
Is it necessary for hadronic calorimeters to be made up of heavy materials like iron or copper? If it is, why ?
|
When using Dirac bra-ket notation to make some statement regarding an operator acting on the vectors of a Hilbert space, is it necessary that the basis of the Hilbert space is made up of the eigenvectors/eigenfunctions of the operator? Or doesn't it matter?
|
In the paper arXiv:1307.0411 by Seth Lloyd, Masoud Mohseni, Patrick Rebentrost
on page 3, line 8, it says: Constructing the $\log_2N$ qubit quantum state $| v \rangle = |\vec{v}|^{-1/2}\vec{v}$ then takes... etc.
My question is then: Why is it:
$$| v \rangle = |\vec{v}|^{-1/2}\vec{v}$$ and not
$$| v \rangle = |\vec{v... |
Motivated by this question: If electrons were spinless/scalar bosons, would atomic ground state configurations necessarily have total orbital angular momentum zero?.
Can we make a group-theoretical argument that the ground state of a system of spinless bosons in a centrally symmetric field necessarily has zero angular ... |
In the context of electric field lines, the following is an excerpt from NCERT's Physics Part 1: Textbook for Class XII
Another person may draw more lines. But the number of lines is not
important. In fact, an infinite number of lines can be drawn in any region. It is the relative density of lines in different regions... |
Studies show that manual treadmills burn 30% more calories than automatic ones.
Let's assume that there is no air friction.
The figure is a diagram of the forces acting on a person running on the ground, but it is no different from the principles in the treadmill.
Eventually, the friction force created by the force of... |
Consider the following problem:
A vector field $\boldsymbol{F}(x)$ is defined over a finite region $V$. A functional of the form
\begin{equation}
U = \int_V u(\boldsymbol{F})\ d^3x
\end{equation}
is to undergo the variation with respect to both $x$ and $\boldsymbol{F}$ but with the constraint that the divergence of the... |
Observation:
Due to decoherence, the reduced density matrix of a system that has interacted with an environment might look like this:
$$a_0a_0^*|0\rangle\langle 0|+a_1a_1^*|1\rangle\langle 1|+$$
$$a_0a_1^*|0\rangle\langle 1|r+a_0^*a_1|1\rangle\langle 0| r^*$$
One usually says to this, that "no quantum properties" or "... |
Wannier orbitals are not unique and depend on a choice of phase of the Bloch wave functions. This typically leads to people attempting to define Wannier functions such that they are "maximally localised" (see, for example, wikipedia).
Based on Wannier orbitals, one often then defines the Hubbard Model parameters, i.e.,... |
So most people want to ask what happens if you go super-close to the speed of light and try to go a bit faster. I want to know what happens if you stop accelerating at close to $.99c$. Not decelerate, just stop accelerating and coast at $.99c$. Would the time dilation effects suddenly cease? Would time pass at a simila... |
The very early universe was dense and opaque. During the quark epoch, the entirety of the universe, up to every boundary, was a filled-in ball of QGP. Much like a star is a ball of ionized nuclei that are too hot and pressurized for electrons to interact with, and a neutron star is a ball of hadrons that are too hot an... |
I learn something about the Time evolution of Gaussian wave packet in free space.
if the initial condition is a Dirac delta function at $t=0$, then the wave function is
$$
\psi (x,t)=\frac{1}{\sqrt{2\pi it}}e^{-\frac{x^2}{2it}}
$$
my question is it seems that the square of the modulus of
$$
\left |\psi (x,t) \right |... |
I am reading arXiv:1606.01857 (Maldacena-Stanford-Yang), one of the main papers on Jackiw-Teitelboim (JT) gravity. To derive the Schwarzian action, they use the classical solution for the dilaton, eq. (3.10).
My question is: Why is this ok? Since this is a quantum theory, shouldn't we let the dilaton fluctuate?
I am ... |
I'm studying Majorana Fermion Surface Code for Universal Quantum Computation by
Sagar Vijay, Timothy H. Hsieh, and Liang Fu. There they consider the Majorana plaquette model on an hexagonal lattice.
There are Majorana fermions ($\gamma_n$) at each lattice site and the Hamiltonian is $$H=-u\sum_p \mathcal{O}_p,$$ where ... |
It's a simple but confusing issue for me.
Let's think about the following situations.
The same person (It has exactly the same physical properties.) pushes an object of M1 and M2 (M1 and M2 have different values.) in mass by the same force and distance, respectively.
For an external stationary observer, that person's v... |
In Griffiths' Introduction to Electrodynamics chapter 7, he states Ohm's law:
$$\vec{J}=\sigma \vec {E}$$
He also states that if
$$\frac{\partial {\rho}}{\partial {t}}=0$$
then $$\frac {1} {\sigma} \vec {\nabla} \cdot \vec {J} = \vec {\nabla} \cdot \vec {E} = 0$$
However, if we assume that
$$\vec {J} = \rho v \hat {z}$... |
From statistical mechanical theory, a simple model for a hypothetical hard-sphere liquid
(spherical molecules of finite size without attractive intermolecular forces) gives the
following expression for the Helmholtz free energy $A$ with its natural variables $T$, $V$, and $n$ as the independent variables:
$$
A = -nRT \... |
I want to find the matrix B in $$ε(x) = B(x) * u$$ where u is nodes displacements. $$B(x) = d^2/dx^2[N(x)]$$ where [N(x)] is a matrix of shape functions. The stiffnes matrix can be defined as $$K = \int_{0}^{L} [B^T][D][B] \,dx$$
with some coefficient.
The shape functions coefficients are not constant though. I thought... |
This is for a Fluid dispensing system. To be used to dispense a paste-like material.
The issue is that I need a specific amount of material to be within tolerances.
The system dispenses from a Gantry unit which moves in the x-y directions Z is fixed.
The Gantry moves at a speed of 6 in/s (152 mm/s)
The material is in a... |
I am learning about von Neumann entropy and I understand that it should vanish for a pure state. I tried to calculate it for the pure state whose wavefunction is $$|\psi\rangle = \frac{1}{\sqrt 2} (\lvert\uparrow\rangle + \lvert\downarrow \rangle)$$ and whose density matrix is
$$\rho = \frac{1}{2} \begin{pmatrix} 1 & 1... |
Consider a force F acting along the x-axis applied to a directed lever arm L parallel the y-axis, and with the conventional torque T parallel to the z-axis, with the three vectors a right-handed triad. It is now very well known that a torque is a tensor not a vector. It is a three-dimensional structure that acts in th... |
In electromagnetism, we can solve Laplace and Poisson equation using Bessel functions. But my question is why don't we use Bessel functions to solve these equations for gravitational potential?
|
Good day,
I am curious in regards to 3D metal printing. Can magnetic or electrical fields affect density, form or crystallization form in molten metals? I am interested in fine tuning the precision of 3D metal printing.
Thank you for your help.
|
Consider the stress energy tensor of dust matter fields
\begin{equation}
M=\begin{pmatrix}
c^2&cv_x&cv_y&cv_z\\
cv_x&v_xv_x&v_xv_y&v_xv_z\\
cv_y&v_yv_x&v_yv_y&v_yv_z\\
cv_z&v_zv_x&v_zv_y&v_zv_z
\end{pmatrix}.
\end{equation}
The determinant of the matrix
\begin{equation}
\det M=0.
\end{equation}
Consider the specialty o... |
In Peskin&Schroeder they explain in a graphical way why the Schwinger functional generates only connected diagrams. However I don‘t understand why they get 2 diagrams since the first diagram is just a symbol for the propagator $\langle\phi(x)\phi(y)\rangle$.
|
Upward spin (lift) applied to a tennis ball will shorten its trajectory.
Are mathematical calculations and actual experimental results on this available somewhere?
If not, does anyone know how to relate the ball's rotation speed to the (modified/distorted) parabola of its trajectory?
My thinking is that there must be a... |
At which rate does the visible matter density in galaxies decrease when moving away from the galactic center?
|
Let's define the intensity of an emission line $I(v',J'\rightarrow v'',J'')=N(v',J')A(v',J'\rightarrow v'',J'')$ as the number of photons emitted per unit time per unit volume due to the $(v',J')\rightarrow (v'',J'')$ line. Also, let's define the intensity of an emission band $I(v'\rightarrow v'')=N(v')A(v'\rightarrow ... |
I am unable to obtain the internal energy of the BTZ black hole. Recall its metric, which is given by
\begin{align}
ds^2=-N^2(r)dt^2+\frac{dr^2}{N^2(r)}+r^2\left(d\phi+N^\phi(r)dt\right)^2\,,
\end{align}
where the Lapse and shift function are
\begin{align}
N(r)=\left(-8MG+\frac{r^2}{\ell^2}+\frac{16G^2J^2}{r^2}\right... |
When quark gluon plasma is created during heavy ion collisions, the QGP exists extremely briefly before hadronizing--the process where the QGP cools and quarks combine to form colorless hadrons. A similar hadronization process occurred shortly after the Big Bang, when temperatures cooled enough for protons and neutron... |
Weizmann Lectures on the Numerical Conformal Bootstrap 1907.05147 Eq. 3.19
\begin{equation}
g_{\Delta,l}(u,v)=
g_{\infty,l}(\Delta, u,v)+\sum_{I}\sum_{m\in\mathbb{B}_{I}} \frac{c_{I,m}}{\Delta-\Delta_{I,m}} g_{\Delta_{I,m}+m,l_{I,m}}(u,v)
\end{equation}
What's the set $\mathbb{B}_I$?
Also, wasn't
\begin{equation}
g_{\i... |
It is often said that there's more matter than anti-matter, How do we know that there is more matter,
Can't there be a galaxy made up of antihydrogen? Will that galaxy be any different from ours?
How do we know that there is asymmetry?
|
I posted a similar question yesterday, but the question hasn't been solved yet, so I'm posting a similar question again. (sorry for similar question..)
Let me write my interpretation of the situation below.
First case) On frictionless ice, 50kg of people exert force on 200kg of objects. (Initial speed is zero.)
If the ... |
I'm attempting to solve Exc. 3.4e from Peskin and Schroeder, which is about Majorana Fermions. We are asked to diagonalize the Hamiltonian in terms of creation and anhiliation operators. Now I'm studying a solution by hong-Zhi Xianyu https://zzxianyu.files.wordpress.com/2017/01/peskin_problems.pdf, where I'm having tro... |
I was studying about projectiles in the section of 2D Kinematics, where I came to know about the ground to ground projectiles. I got to know that for having maximum range in ground to ground projectiles (such as in the case of throwing a javelin), there should be an angle of 45° with the ground. But I also came to know... |
Symmetry of this system has been discussed here but I'm still confused.
Consider a $N$-dimensional isotropic harmonic oscillator, with hamiltonian
$$H = \hbar \omega \left(a^\dagger_i a_i + \frac{N}{2} \right).$$
$a^\dagger_i$ and $a_i$ being the creation and annihilation operators for dimension $i$, and using summatio... |
I'm curious whether the reversal of spin number in antiparticles vis-a-vis their matter counterparts would have a corresponding reversal of the chirality of structures made of antimatter (over scales where gravity is insignificant). For instance, natural glucose is right-handed; if we assembled a perfect antimatter cop... |
I need to prove that under an infinitesimal coordinate transformation $x^{'\mu}=x^\mu-\xi^\mu(x)$, the variation of a vector $U^\mu(x)$ is $$\delta U^\mu(x)=U^{'\mu}(x)-U^\mu(x)=\mathcal{L}_\xi U^\mu$$ where $\mathcal{L}_\xi U^\mu$ is the Lie derivative of $U^\mu$ wrt the vector $\xi^\nu$.
I have performed the followin... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.