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How does Garrett Lisi's "Exceptionally Simple Theory of Everything" contain the Higgs Boson and Graviton? Let's say that $E_8$ breaks down like this:
$$E_8 \rightarrow E_6 \times SU(3).$$
Then the representations breaks down like this:
$$248 \rightarrow (78,1) \oplus (27,3) \oplus (27,3) \oplus (1,8).$$
The first repre... |
I recently learned how magnetic forces on point charges can be viewed as purely electric forces on point charges in the appropriate reference frame. This got me thinking if there was a similar effect with gravity. Consider an infinite, massive plane of mass density $\sigma$. If we have some point mass, $m$, located in ... |
I want to make a simulation of the stopping of Muons in liquid water that, instead of considering they lost exactly the amount of energy predicted by the $dE/dx$ curve at each iteration, sorts an amount of energy loss according to an energy loss distribution W(E), to make it more probabilistic.
And I've found some info... |
Here is a question I have always wondered about.
I have a family member that dislikes drinking hot beverages (e.g. coffee, tea). https://www.flickr.com/photos/adamcohn/16290609394
This family member after preparing the drink will stretch their hand as high up as they can .... and pour it from a large height into anot... |
Reading the paper "Astro2020 Science White Paper
Where are the Intermediate Mass Black Holes?", and the plot in Fig.1, page 5, it seems LISA can see IMBH beyond 100 Gpc...Since the observable universe is about 14-50 Gpc, does it mean LISA can observe beyond the observable Universe?
|
Just a random question out of interest.
When you hear an explosion, e.g. a firework, firecrackers etc, from far awa how does the sound reach our ears so quickly?
The speed of sound in air is like 300m per second, and if a firework 2 km diagonally away from me in the sky explodes, then mathematically it should take 2000... |
In the introduction the authors state that the reason for presence of arbitrary functions of time in the general solution of E.O.M is a key property of the gauge theory.
“In a gauge theory, one cannot expect that the equations of motion will determine all the dynamical variables for all times if the initial conditions... |
Normal force is the component of a contact force that is perpendicular to the surface that an object contacts.
Above is the Wikipedia definition of Normal Force. The confusion is regarding how the following scenario satisfies Newton's Third Law.
The scenario is:
A book is placed on a table and the following forces ar... |
For example we work with a 2d scalar field $\phi$. I guess $\phi$, $\partial_z\phi$, $\partial_{\bar z}\phi$ are fields, are there more? Is it true that all fields are in the form of $\partial_z^i\partial^j_{\bar z}\phi$? Are there any context explaining why do we call those 'fields'?
More exactly, in an OPE: $\phi_i(x... |
In our common understanding, ice needs to be above 0°C to melt.
I have now done an experiment: a piece of glass covered with ice on one side and a heating module on the other end. Placing it in a -20°C environment, the heating module starts working and after about 10 minutes the ice melts and disappears.
so my question... |
in Sidney Coleman's paper More about massive Schwinger model (PDF). Section 2 "The origin of $\theta$" P.242 (beneath the eq. 2.5). Discuss about some differences between 1+1D & 3+1D electric field with background field $F$, Coleman's paper said that:
In 3+1D, "it is always energetically favorable for the vacuum to em... |
Let's suppose that $\psi$ is a field so that $$\psi\in\Gamma^\infty(\pi):=\{\psi\in C^\infty(M,E)\ |\ \pi\circ\phi=I_M\}$$ where $E$ is a spacetime bundle over spacetime $M$ and $\pi : E\rightarrow M$ is projection map. Variation of the field is then defined as a family of smooth maps $$\hat{\psi} : M\times (-\epsilon,... |
I recently read the PBR Theorem and from what I understand it addresses one of the old problems regarding quantum state completeness, one for which there are three possibilities (correct me if am wrong here):
A physical state $\lambda$ corresponds to several quantum states $\Psi_{i}$
Multiple physical states $\lambda... |
Recently I've been thinking about $1d$ Path Integrals of some theories with non-standard Lagrangians. The adjective non-standard meaning that the Lagrangian $\mathcal{L} \neq \frac{1}{2} m \dot{x}^2 - V(x)$, and has a more general form $\mathcal{L}= \mathcal{L(x, \dot{x}, \ddot{x}, \dots)}$.
In my understanding of the ... |
When an ideal dipole with constant current $\vec{m}$ is in a magnetic field, its "potential" energy is $-\vec{m}\cdot\vec{B}$, which may be used to derive the magnetic force acting on the dipole as $-\nabla U$. Yet at the same time there's the energy needed to establish currents as $1/2 ~ ~\Sigma I\phi$. If I apply thi... |
I know there is a peak in the current flowing through the heterostructure when the voltage bias applied $U$ equals 0.05 V. From what I know this should align with the energy being equal to that of the ground state in the well. How would I then determine the distance between the barriers (or the width of the well betwee... |
My question is:
Why do conjugate points exist on globally hyperbolic manifolds, satisfying the strong energy condition?
We define M to be globally hyperbolic if it posseses a cauchy surface and a pair of points $p,q$ are said to be conjugate if there exist a Jacobi field which is not identically zero but vanishes at $p... |
Context
In all string textbooks and lecture notes, they derive the CKV on the sphere by considering the flat plane first, i.e. $(\mathbb{C},\delta_{\mu\nu})$. Then, write it in complex variables
$$z = x^1 + ix^2 $$
Consequently, the metric is then
$$ds^2 = dzd\bar{z}$$
As a result, the conformal transformations are ge... |
I'm currently studying statistical mechanics. The book the class is following is "Statistical Mechanics, Third Edition" of Pathria and Beale. Chapter 3 presents two approaches to canonical ensembles:
a more thermodynamical approach, where the ensemble is described by a system with fixed $N$ and $V$ in thermal contact ... |
Here's the description of problem I wanna talk about. (It is from Morin's Classical Mechanics)
There is a solution for this problem in the textbook :
I run into problem with this solution, even though I think it should break too (I can mention why I think that way, but my question is about understanding the solution.)... |
It is said that in the double slit experiment one will prevent the interference of the photon with itself by simply observing which path the photon.
Here is a very first Google result for "double split experiment":
To find out, you might place a detector by the slits, to see which slit an electron passes through.
htt... |
I'm not a radiation physicist. Kilovolt-peak appears to be used as a unit, with descriptions such as "80 kVp". Should this be typeset as a single unit written "Vp", similar to e.g. "Gy" for Gray, or with the "p" as a subscript, or in some other way?
As someone not in the field, I'm not sure how to judge whether papers ... |
Drop a heavy incompressible object into water and it would splash and then presumably reach a certain terminal velocity where acceleration is nill.
If you dropped a heavy incompressible object into a sufficiently deep thixotropic, or shear thinning fluid, that enabled movement of the object in the first place, what wou... |
Suppose there is a spherical shell made of a perfectly conducting material with inner radius $R_{1}$ and outer radius $R_{2}$. A dipole with charges $+q$ and $-q$ separated by a distance $a$ ($a<R_{1}$) is placed inside the shell.
What would the electric field be inside and outside the shell? What would the charge indu... |
I am quite new to this topic. Please bear with me.
Suppose we are given a transformation of both time and space coordinate's derivatives as
$$
\partial_t\to D_t=\partial_t-f(t,x)\partial_t\\
\nabla\to \mathbf{D}=\nabla+\mathbf{F}(t,x)\partial_t \tag{1}
$$
$f$ is a scalar field and $\mathbf{F}$ is a vector field. Is the... |
Can someone give me some steps on showing the last line.
From the line, $$-\int d^3x \space \epsilon_{abc} \space [ (\nabla^2\phi_b) \phi_c - m^2\phi_b\phi_c ] $$ I cannot actually see how could this end up with the expression,
$$ \int d^3x \space \epsilon_{abc} \space \nabla\phi_b \cdot \nabla\phi_c .$$
One idea that... |
As of right now, whenever right now happens to be, has anyone identified any promising experiments capable of distinguishing between the Copenhagen interpretation and the Pilot Wave interpretation of Quantum Mechanics? If so, has any progress been made on performing these experiments?
|
Right now I am swinging a bottle of water in a tight circular motion to form a vortex, the vortex will last quite a while after I stopped swinging it. The vortex will took the shape of a funnel in 1g at sea level, but if I were to repeat the same experiment in free fall (inside a space station) would the funnel shaped ... |
I came across this theorem in Morin's classical mechanics:
Theorem 7.1 The angular momentum (relative to the origin) of a body can be found by treating the body as a point mass located at the CM and finding the angular momentum of this point mass (relative to the origin), and by then adding on the angular momentum of t... |
Say that the current source is doing whatever it needs to do to output $1$A and that the battery is a $3$V battery. For simplicity, say the resistor is $1\Omega$.
I get that since we have $1$A through the resistor, the drop has to be $1$V. I don't how to find the potential difference between some point before the batt... |
Has there been any experiment showing that velocity of light in solids changes in if magnetic field is introduced? We know that the polarization of light traveling through some solids may be altered by the presence of magnetic field but is there any experimental evidence that the velocity may be altered as well?
|
In the proof that the speed of light is a constant we make the assumption that space at large scales is homogeneous, but there are patches of space where the density is higher and there are patches where it's lower. Does that mean that it is a little bit different in these patches? Maybe light could light travel faster... |
Given a laser operating at a wavelength $\lambda = 1.084 \mu m$ on two longitudinal modes $300 MHz$ apart, I have to find the minimum free spectral range $FSR_m$ necessary to correctly measure the two modes. I've chosen to use a free spectral range $FSR >2B$ where $B$ is the bandwidth of the intensity spectrum to measu... |
I'm having trouble understanding why the dispersion relation $\omega(\vec{q})$ is extremal at the boundaries of the first Brillouin zone.
I understand why the dispersion relation is symmetric around zero $\omega(\vec{-q}) = \omega(\vec{q})$ and that the translational symmetry of the crystal implies that $\omega(\vec{q}... |
Suppose a diathermic movable piston separates an adiabatic container into $2$ parts. Thermodynamic parameters of gases in the two parts are $p_1,v_1,t_1$ and $p_2,v_2,t_2$. We assume quasi static processes.
If we apply first law of thermodynamics to these two parts separately and take into account that heat lost by one... |
I would like to preface this by stating this type of research is my hobby not my profession.
If I understand the basic explanation correctly, energy tends to spread out evenly within a closed system given enough time and matter tends to clump together due to the fundamental interaction that we refer to as gravity
Based... |
Let's say there are two objects.. one the size of a bowling ball weighing 10 pounds.. and the other object is the earth's moon.. they are both the same distance from the earth.. now.. wouldn't the earth pull the bowling ball to it faster than the moon because the moon has a much larger gravitational pull of its own to ... |
This isn't a question for a class, it's just driven by curiosity.
I hope you like it.
Let's consider a particle in a box with infinite potential barriers, but now the walls can oscillate/move.
Does anyone ever heard of such a problem? I can't find any literature mentioning that.
However, my actual question is, how coul... |
We understand that quantum particles have properties like 'spin'. And upon observation, the value of this property is determined. Before observation, the value is non-determined and the wave function contains all values.
So my question does the property itself exist before observation? Does 'spin' itself exist?
It seem... |
Suppose you have have acceleration and angular velocity for a rigid object but unknown initial orientation, velocity and position.
Can you integrate the known data in such a way that it's easy to update the system when the initial conditions become known?
For position with a fixed orientation it's straightforward but t... |
I am trying to understand the explanation of Bose-Einstein condensation for non-interacting bosons given in Piers Coleman's "Introduction to Many-Body Physics", pg. 85-86. Coleman first writes that the density of a gas of bosons at finite temperature is given by
$$\rho = \int \frac{d^3 k}{(2\pi)^3} (e^{\beta (E_k - \mu... |
Consider two points in a rigid body and their velocities at a particular angle to the horizontal. The horizontal components of velocities must be equal so as to satisfy the basic definition of a rigid body. Can we also say that their vertical components must be equal so as to maintain the gap?
|
Can't you construct a Gaussian surface small enough to surround only one of the interior protons, thus the surface has a charge enclosed and a electric field by Gauss's law.
|
My question is, given the above statement, why electromagnetic waves attain different speeds in media other than vacuum even though they are of the same type and propagate in the same medium?
|
I'm just curious if binary stars are low over the horizon and the conditions are just perfect for the formation of rainbow, would I see a single rainbow, double rainbow or two rainbows intersecting each other?
|
We usually want to study the infinitesimal transformations on the action which depends on the field $\phi(x)$ and its derivatives. Such transformations may in general be written as,
\begin{equation}
x'^\mu = x^\mu + \epsilon_a \frac{\delta x^\mu}{\delta \epsilon_a}\tag{1}\label{1}
\end{equation}
where {$\epsilon_a$} is... |
I have a simple question that's been on my mind for a while. If both current is proportional to voltage ($I \propto V$) and voltage is proportional to current ($V \propto I$), are they actually saying the same thing, or are they different statements? I have the same question about stress and strain: if stress is propor... |
Fi acts on the entirety of the object, Mi is the collection of all particles in the object. So, it makes sense that ai is the collection of all tangential accelerations of the particles. I don't know if my assumption is correct because the book is too vuage. It might be because I'm missing something though. Many thanks... |
The Pauli term is roughly given by
$$M_{\mu\nu}F^{\mu\nu} = K\cdot E + J\cdot B$$ where $K$ is the boost and $E$ is the electric field and $J$ is the angular momentum and $B$ is the magnetic field. We know the second term to be the magnetic moment of the particle but what about the first term? Is it the ''electric mome... |
The question is:
A vertically hanged chain with the upper end attached to a fixed point. I try to find the normal modes under the small $\theta$ condition.
Consider the mass $\mathrm{d}m$ with distance $s$ away from the fixed point(along the direction of the chain), the coordinate is:
$x=\int_{0}^{s}\sin{\theta}\ \math... |
I'm having difficulty understanding how to physically compute how a covector changes under Lie transport.
Suppose on $\mathbb{R}^2$ I have a vector field $V=x\frac{\partial}{\partial x}+y\frac{\partial}{\partial y}.$ Suppose also that I have a covector, for example $\omega=2dx$ at the point $(1,1)$. I would like to com... |
I am following chapter 9 of the Rammer's book on Field Theory (which you can find here: https://www-thphys.physics.ox.ac.uk/talks/CMTjournalclub/sources/Rammer.pdf). I am referring to section 9.2.2, page 274, that deals with the derivation of the Dyson-Schwinger equation (of a cubic theory) using diagrammatic technique... |
I have found an interesting sentence in my book on electromagnetism:
given the wave equation for electric field in empty space
$$\nabla^2 \vec{E} - \epsilon_0 \mu_0 \frac{d^2 \vec{E}}{dt^2} = 0$$ and similar for magnetic field
these equations are obtained from the third and fourth maxwell equation, however they are not... |
I do understand how oscillating (accelerating) charges emits Electromagnetic waves through the propagation of kinks(back and forth) in the electric field of the oscillating charge which propagates at the speed of light.
But how does linearly accelerating charges emits "waves" as I can't see how a linearly accelerating ... |
Quantum field theory in curved spacetimes is often described in the algebraic approach, which consists of describing observables as elements of a certain $*$-algebra. To recover the notion of a Hilbert space, one represents this algebra as operators acting on said Hilbert space. Given a state on the algebra, the GNS co... |
I am having trouble simplifying this electric circuit. Should I neglect R1 in the simplification or not?
|
If I consider an object moving with a non-uniform circular motion with constant angular acceleration, the tangential acceleration modulus remains constant, while the centripetal acceleration modulus changes ($a_c=Rω^2$). Does the angle that the total acceleration forms with the centripetal change? If so, does it mean t... |
Consider a conducting rectangular strip of length $L$ (along x-axis) and width $W$ (along y-axis), with a potential difference (rather EMF $\int E.dx$) V(t) applied. We can assume that V(t) changes sufficiently slowly to treat the problem ``adiabatically". That is, I am hoping we can solve the static problem for a cons... |
I am trying to solve this problem;
minimizing the functional $\int\sqrt{y^2+y\prime^2+z\prime^2}dx$ with the constraint $y+z=1$ (Here $y\prime=dy/dx$, $z\prime=dz/dx$, and $x$ is the only independent variable).
I tried using Lagrangian Multipliers to minimize the function $$f(y, z, y\prime, z\prime; x)=\sqrt{y^2+y\pr... |
I need to compute the scattering amplitude for the process $\gamma\gamma\to e^+e^-$ at tree-level in QED. In my notes, it is written that there are two Feynman diagrams for this process, but I only seem to find one. My reasoning is the following:
The incoming photons are distinguishable (as I think all incoming partic... |
Reading the CP symmetry section from Griffiths elementary particles book, 2nd revised edition, page 146.
As mentioned in the above picture the neutral kaon and its antiparticle form linear combinations that are eigenstates of CP operation. To conserve CP, $K_1$ must decay to 2 pions and $K_2$ must decay to 3 pions. I ... |
Given a Lagrangian using the standard cartesian coordinates.
$$ \mathcal{L} = \frac{1}{2}m(\dot{x}^2 + \dot{y}^2) - \frac{1}{2}k(x^2 + y^2) $$
How to move to the hyperbolic coordinates given as
$$2 x y = \mu $$
$$ x^2 - y^2 = \lambda $$
One way is to invert the expression of the hyperbolic coordinates and express $x$ a... |
I am working through d'Alembert's solution to the 1+1D wave equation using the substitution of canonical coordinates. I have an initial condition of: $$u_{t}(x,0) = g(x) $$ with a general solution containing the following two arbitrary functions: $$u(x,t) = \phi(x-ct) + \psi(x+ct)$$ These two functions are composite fu... |
Reasons for the existence of a magnetic force can be found in the rest frame of a moving electron next to a current carrying wire as explained in Chapter 5.9 "Interaction between a moving charge and other moving charges" of Purcell: Electricity And Magnetism.
However, I am looking for an explanation in the lab frame, s... |
I came across many definitions of the precision of a measuring instrument such as, "a precise measuring tool is one that can measure values in very small increments" and "The precision of the instrument that is used to take a measurement is reflected in the smallest measure that the instrument can make". However, none ... |
On the first page of his first paper in series "Quantization as an Eigenvalue Problem", Schrödinger begins with
$$H(q, \frac{\partial S}{\partial q})=E$$
and then takes a change of variable that I don't understand its motivation:
Here we now put for $S$ a new unknown $\psi$ such that it will appear as a product of r... |
I am looking for a book of which I have one chapter. I tried to find this book by references and by copying the text in the GPT chat however without success.
One chapter was sent to me by a professor as a study aid however he has no idea who the author is.
It is chapter 12 which covers topics related to plasmons.
I don... |
I have some doubts regarding my personal interpretation that i was contemplating about in the context of Wigner's friend experiment (also tested in the laboratory).Could it be that a system is always in a superposition, and when we perform a measurement, we obtain a definite value due to the interaction, but after it, ... |
In a mixture of a cylindrical particle and the carrier fluid, what exactly particle inertia refer to? (let's neglect gravitation force and Brownian motion).
When the size of particles are small (particle Reynolds number around unity), it is often assumed that the force on the particle is a linear function of slip veloc... |
I have a fundamental question in statistical mechanics that I can't wrap my head around.
When we speak about the probability of a SYSTEM being in macrostate with energy E we calculate this by:
$$ P(E) = \frac{e^{-\beta E}}{Z} $$
where Z is the partition function.
But if we zoom in and look at the probability of a speci... |
Question:
A square of side length a with uniformly distributed positive charge lies on the yz-plane with its center at the origin. What is the graph of the electric field along the x-axis?
Below is the correct graph for the question.
According to my textbook, this is the correct graph for electric field. However, I a... |
I'm reading Climbing the Mountain by Mehra, in which he explains Schwinger's source theory by an example. He appears to end up giving an explicit form for the effective action of QED and I don't understand the reasoning.
He starts by giving the vacuum persistence amplitude in the presence of photon source $J$ and elect... |
I'm having difficulties proving the following identity using the lowering operators $(L_{-})^n$ in the context of spherical harmonics:
$$
Y_{L}^{-M}(\theta, \phi)=(-1)^{M}Y^{*M}_{L}(\theta, \phi)
$$
I've attempted other strategies (like using $L_{+}$ instead), but I can't seem to arrive at a convincing proof. I apprec... |
I understand how a polarised wave can have a local phase, in that the horizontally polarised portion of the wave may not oscillate in the same phase as the vertically polarised portion, but how does an electron qubit have a local phase, considering it spins either clockwise or anticlockwise, or in some orientation in b... |
It is known that when a Klein-Gordon (KG) field is expressed in plane wave basis, then the Feynman propagator defined as
$$\Delta_F(x-y)=\langle 0|T\{\phi(x)\phi(y)\}|0\rangle$$
equals the Green's function for the KG Operator. However, we can take a different approach using the Schwinger-Dyson equations (see for instan... |
When solving the Schrodinger equation of the harmonic oscillator in one dimension you encounter the hermite differential equation:
\begin{equation}
\left[\frac{d^{2}H}{d\xi^{2}}-2\xi\frac{d H}{d \xi }+\left(\lambda-1\right) H\right]e^{-\xi^{2}/2}=0.
\end{equation}
We can find a solution to this equation in the form of ... |
A vibrating string with fixed endpoints, such as on my fiddle, may be bowed (see Helmholtz motion, see stick and slip) with very little to a certain amount of pressure and proximity to the bridge (the combination hereafter abbreviated as amplitude) with un-noticeable change in pitch before beginning to sound sharp (mor... |
If two operators $ A $ and $ B $ are compatible then their corresponding operators $ \hat{A} $ and $ \hat{B} $ share a common set of eigenfunctions. The eigenvalue-eigenfunction equation for each operator is:
$$ \hat{A} \phi_n = \alpha_n \phi_n $$
$$ \hat{B} \phi_n = \beta_n \phi_n $$
Let's say these operators are comp... |
One could say we're taking advantage of friction, but I want to dig deeper down to atomic level: what's the process or chain that happens when one erases?
Edit: subatomic -> atomic
|
Let's say I have manufactured a prism from a non-dispersive medium, then light coming from air incident on the prism wouldn't split into colours, right? I mean light still changes direction, but all colours would change direction by the same amount.
|
In a $d$-dimensional Hilbert space, a channel is a completely positive trace preserving map, and a completely dephasing channel $\Delta$ (implicitly defined with respect to a fixed orthonormal basis $\{|i\rangle\}_{i=1}^d$) acts on a state $\rho$ according to
\begin{equation}
\Delta(\rho) = \sum_{i=1}^d |i\rangle \lang... |
I sit in a space shuttle in zero gravity condition.
I have a spoon in one hand and the jar of marmalade in the other.
I take marmalade with spoon.
If I shake it very hard, will the marmalade detach from the spoon?
Yes, why, no, why not?
|
Most $E_8$ gauge theories follow this breaking chain:
$$E_8 \rightarrow E_6 \times SU(3)_{Gen}.$$
How does the $E_6 \times SU(3)$ group break down through $SO(10)$, the Pati-Salam Model or the Minimal left-right symmetric model. (More importantly, how does the $SU(3)_{Gen}$ group breakdown and at what stage.) And also,... |
When I feel the slight gravitational pull of one particle that is in a state of superposition and I measure the exact pull at any given instant does the wavefunction collapse? If particle A constantly receives small differences in gravitational pull from particle B isn't particle A constantly observing the position of ... |
So my question is that,what actually the apparent position of let's say a coin in water seen by us is??
It's a small experiment in textbooks that take a coin in a shallow and wider bowl and mark the position from where you are not able to the coin. And then put water in the bowl upto neck and then go back to that posit... |
The textbook "Modern Particle Physics" by Mark Thomson on p. (98) reads:
In the left plot, an electron of energy $E$ emit a photon with energy $2E$ and, to conserve energy, produces an electron with energy $-E$, which being a negative energy solution of the Dirac equation propagates backwards in time.
Now, since the... |
I have heard many lectures claiming that even a single electron being shot toward the slits will eventually lead to construction of an interference pattern. The rationale for firing one electron at a time is that by using a single electron the possibility of the electron interacting/interfering with other electrons fro... |
In David Tong's lecture "Quantum Field Theory" - Lecture 2, he said that
"In Quantum mechanics, position is the dynamical degree of the particle which get changed into an operator but in Quantum Field Theory, the position will be just considered as label"
So, I was wondering: Why?
|
In 'Thermodynamics' , the section under "heat engines" mentions, that, it is practically impossible to create an engine which can operate with just a heat source and no heat sink present. Why isnt that possible? Cant a ship just take heat from the ocean to drive itself, without burning fuel? Also, why is it not possibl... |
Would audible sound be blocked by a wall of ultrasonic sound (see diagram below)? Since the ultrasonic speaker gives rise to fast vibrations of the air, would the audible sound still pass through it? When the audible sound passes through the ultrasonic waves, it might combine with the ultrasonic waves, generating many ... |
Imagine the familiar setup of the double slit experiment using laser but it is submerged in a tank filled with water, would there be any interference pattern? I also read somewhere that tonic water contains quinine which glows in black light or UV-A, what if I replace the water in the tank with tonic water and switch t... |
If there were no Hawking radiation (and no black hole radiation of any kind, or any way for black holes to reduce in size or disappear), then it seems a black hole would represent an irreversible end state of any matter or energy that became dense enough. They would only grow over time.
If this were the case, it seems ... |
Suppose, I look at the $SO(3, 1)$ generalization of $H = \frac{p^2}{2m}$, i.e. $$H = \lambda P^{\mu}P_{\mu}$$ where $P^{\mu}P_{\mu}$ is a $SO(3, 1)$ invariant object and $\lambda$ is some dimensionful constant (It's just hypothetical. It may not describe a physical system as such.). If I consider the quantum partition ... |
In appendix C.4.3 of "Anyons in an exactly solved model and beyond", Kitaev provides a proof of the fact that when the Chern number is odd, a vortex in the gauge field accompanies an unpaired majorana mode.
The original gauge configuration that appears in the quadratic hamiltonian of majorana operators is B, while the ... |
Reading T violation from Perkins High Energy Physics, 4th ed, pp 82.
Here I don't understand the definition of last 4 quantities, magnetic and electric dipole moments, longitudinal and transverse polarisations. Why they are defined in that way?
I know the definition of dipole moments when a charge/current placed in an... |
Consider a metal rod being heated. As metal rod is a good conductor, it spreads heat all through it. If so I think all the linear,area and cubical expansion takes place simultaneously practically. Am I right?
|
Consider a real Klein-Gordon field $\phi$ in a globally hyperbolic spacetime, with metric $g_{\mu\nu}$.
The covariant Klein-Gordon equation is
$$(g^{\mu\nu}\nabla_{\mu}\nabla_{\nu}+m^{2})\phi=0$$
Let $V$ be the vector space of all real-valued solutions to this equation.
Define the following bilinear form:
$$(f,h):=\int... |
I am taking the course "Analytical Mechanics" (from on will be called "AM") this semester. In our first lecture, my professor introduced the notion of generalized coordinates. As he presented, we use generalized coordinates when we have constraints on the system (i.g. being on a sphere). When we have $M$ particles (in ... |
In section 2.4 of Conformal Field Theory by P.D.Francesco, and others, it has discussed the infinitesimal transformation on spacetime and field,
$$x'^{\mu} = x^{\mu} + \omega_{a}\frac{\delta x^{\mu}}{\delta \omega_{a}}$$
$$\Phi'(x') = \Phi(x) + \omega_{a}\frac{\delta \mathcal{F}(x)}{\delta \omega_{a}}\tag{2.125}$$
Here... |
I'm a mathematician who's trying to understand the meaning of Algebraic Bethe Ansatz. What I understood is that when dealing with quantum integrable models (like XXZ Heisenberg spin chain), one is interested in showing that there are conserved quantities (ie operators that commute with the Hamiltonian).
My questions ar... |
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