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7
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0answers
108 views

Simple argument for unexpected behavior in SUSY model

Consider a supersymmetric theory with 3 chiral superfields, $X, \Phi_1$ and $\Phi_2,$ with canonical Kahler potential and superpotential $$ W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$ ...
6
votes
0answers
153 views

Why dimensionality of the Electric Charge varies with the spacetime dimensions?

The point is: We can find via dimensional analysis that the electric charge dimensionality varies with the dimension of space-time. $$[\text{charge}] = eV^{(3-D)/2}$$(You can see below the way I did ...
6
votes
0answers
91 views

Is the uniqueness theorem correct in superconductivity?

There is an uniqueness theorem in electromagnetism. It says that the solution of Maxwell's Equations is determined uniquely by boundary conditions. We can treat superconductivity as a completely ...
6
votes
0answers
307 views

Find $x$ operator given $p$

This is problem $1.2$ of Molecular Quantum Mechanics by Atkins, 4th edition. I'm given the momentum operator $$p=\sqrt{\frac{\hbar}{2m}}(A+B)$$ with $$[A,B]=1$$ and I need to find $x$ in this ...
5
votes
0answers
187 views

Hamiltonian function for classical hard-sphere elastic collision

I'm trying to find the Hamiltonian function for a system consisting of a single particle in one dimension colliding elastically with a wall at x = 0. Everything I've read on the topic (e.g. this ...
4
votes
0answers
55 views

Tricks for Computing Riemann Curvature Tensor with Levi-Civita connection

I am new to differential geometry, so far it seems to me that computing the Riemann tensor tends to be a rather tedious task, I wanted to know whether there are some tricks that I am missing. In ...
4
votes
0answers
43 views

A question about deriving Eq. (6.2.13) in Polchinski's string theory book volume 1

I have a question about deriving Eq. (6.2.13) in Polchinski's string theory book volume I. It is claimed that Now consider the path integral with a product of tachyon vertex operators, ...
4
votes
0answers
99 views

Show that the Laplace-Runge-Lenz vector is conserved using poisson brackets

(I realise similar Phys.SE questions already exist but there is no answer with the Poisson bracket notation, I'll take this down if someone lets me know I should have commented in the existing ...
4
votes
0answers
52 views

Wall stress of a hexagonal pressure vessel

Problem: I want to calculate the stress in the walls of a hexagonal pressure vessel but I can't manage to get coherent results. For long vessels, cylinders are supposed to have the lowest hoop stress ...
4
votes
0answers
141 views

Action of Parity operator on Impulse representation

Is my derivation of the action of the parity operator $\mathbb{P}$ on the $|p\rangle$ representation correct? $$\left( \mathbb{P}\tilde\psi \right)(p)= - \tilde\psi (p).$$ Obtained from $$\left( ...
4
votes
0answers
331 views

How to prove that Weyl tensor is invariant under conformal transformations?

I need to verify that the solution for vanishing Weyl tensor is conformally flat metric $g_{\mu\nu} = e^{2\varphi}\eta_{\mu\nu}$. The most convenient way to show this is to prove that Weyl tensor is ...
4
votes
0answers
78 views

Quantum Cyclotron Frequency - Why is it off by a factor of 2?

Say you have a magnetic field $\vec{B}=(0,0,B_0)$. Then the Schrodinger Equation Hamiltonian for a spin-2 particle of charge $e$ moving in this field is: $$H = ...
3
votes
0answers
185 views

Wald problem 4 of chapter 4

I'm trying to derive equation 4.4.51 in Wald's GR book (the second order correction in $\gamma$ term for the Ricci tensor): where $g=\eta+\gamma$. So ...
3
votes
0answers
70 views

Proof of equivalence of different representations of the $\gamma$-matrices in the Dirac equation

This question concerns the Dirac equation and the $4\times4$ $\gamma$-matrices. The task is to prove that a similarity transformation of the standard $\gamma$-matrix conserves the commutation relation ...
3
votes
0answers
59 views

Feynman Toy Model Constraints on Number of Each Kind of External Lines

(From my homework) In our toy model we have three kinds of spinless particles: $A$, $B$, and $C$. The primitive vertex of decay/interaction is shown below: My actual problem statement says: ...
3
votes
0answers
83 views

Computing the Einstein tensor for a spherically symmetrical metric using the tetrad formalism

I am having some trouble understanding how to use the tetrad formalism. I will start with what I have so far, my question will be after that. I begin with the metric $$ \text{d}s^2 = e^{2a} \text{ ...
3
votes
0answers
182 views

Time Evolution Operator in Interaction Picture (Harmonic Oscillator with Time Dependent Perturbation)

1. The problem statement, all variables and given/known data Consider a time-dependent harmonic oscillator with Hamiltonian $$\hat{H}(t)=\hat{H}_0+\hat{V}(t)$$ $$\hat{H}_0=\hbar \omega \left( ...
3
votes
0answers
67 views

Transformations of gamma-matrices through Pauli matrices transformations

I have the transformation law of the Lorentz group for Pauli matrices: $$ \tag 0 (\sigma^{\mu})_{a \dot {a}}{'} = \Lambda^{\mu}_{\quad \nu} N_{a}^{\quad c}(\sigma^{\nu})_{c \dot {c}}(N^{-1})^{\dot ...
3
votes
0answers
71 views

Virasoro Operators commutation relations

For the commutation relation in quantising the bosonic string $\left[L_n,L_{m}\right]=(n-m)L_{n+m}+\frac{D}{12}n(n^2-1)\delta_{n+m,0}$ we can then calculate this for $m=-n$ in between the vacuum ...
3
votes
0answers
154 views

Practice AP Physics B Exam Question regarding Momentum

I am trying to review momentum for the AP exam coming up. I will be taking the AP Physics C exam for Mechanics, but I was just practicing on any free response questions I could find and I came across ...
3
votes
0answers
69 views

Vertex for quartic interaction of complex scalar multiplet

Since I'm new to QFT and I tend to do a lot of errors during calculations, I would like you to tell me if I got the four-point vertex of the quartic interaction with a multiplet of complex scalar ...
3
votes
0answers
55 views

Property of stress-tensor in flat spaces

Let $T_{ab}$ be a stress-tensor in a flat space satisfying conservation equations. Define $$ P^i=\int T^{oi}d^3x, \;\; D^i=\int T^{00}x^id^3x $$ Can anyone show me how to prove $$ \frac{dD^i}{dt}=P^i ...
3
votes
0answers
91 views

RLC circuit, turning off the voltage source

An RLC circuit (pictured above) is governed by two equations: $$ -iR=-L \frac{dj}{dt} = \frac{q}{C}+V(t) $$ $$\frac{dq}{dt}=i+j$$ q satisfies the equation: ...
3
votes
0answers
69 views

Complex scalar fields conserved charges

I'm currently studying field theory and I'm having some trouble with conserved charge given in field components. If we have a complex scalar action of a field $\phi=(\phi_1,\phi_2)^T$ that is ...
3
votes
0answers
95 views

Why is Clapeyron equation so important?

Context: I'm studying basic thermodynamics. My textbook has a chapter on the Clapeyron equation which, as a reminder, is given by the following formula: \begin{equation} \frac{dP}{dT} = \frac{\Delta ...
3
votes
0answers
55 views

Charge distribution and potential in a 1-dimensional quasistatic system

Suppose you have an 1-dimensional system with a charge distribution $\rho(x)$ (not given) moving with an speed $v(x)$ (not given), calculate the potential $\phi(x)$ and the charge distribution ...
3
votes
0answers
377 views

Killing vectors for 2-sphere as generators of $SO(3)$ symmetry

How to get Killing vectors in a form of generators of $SO(3)$ group symmetry? By using Killing equations for metric $ds^{2} = d\theta^{2} + \sin^{2}(\theta^{2}) d\varphi^{2}$ I got $$ ...
3
votes
0answers
110 views

About Dirac equation in curved spacetime (spherical)

I would like to ask you about the separation of variables of the Dirac equation in curved space-time. The metric is given by $$ds^{2}=-dt^{2}+dr^{2}+r^{2}d\theta^{2}+\alpha^{2}r^{2}\sin^{2}\theta ...
3
votes
0answers
135 views

Fock Subspaces and Weight Vectors

This is my first time taking a physics course (I'm a mathematics major), so I'm encountering a lot of new things, which I'm kind of expected to know. In particular, how to work with Bosons. I've got ...
3
votes
0answers
146 views

Schwarzschild metric in a different coordinate system

In PADMANABHAN, Gravitation (Foundations and Frontiers), Cambridge, p $304$, exercice $7.6$, an example of the Schwarzschild metric in a different coordinate system is given : $$\mbox{d}s^2= ...
3
votes
0answers
83 views

Polchinsky's Evaluation of the One Loop String Path integral

I try to evaluet the matrix M in the Polchinsky's article(Communications in Mathematical Physics,1986, Volume 104, Issue 1, pp 37-47,"Evaluation of the one loop string path integral",Joseph ...
3
votes
0answers
130 views

Irradiation of electronic memory circuits

I am investigating the radiation hardness of electronic memory circuits (EEPROM). The following measurement has been performed: Beam set-up: Irradiation occurred perpendicular to the DUT (device ...
3
votes
0answers
161 views

Angular momentum of particle in dipole magnetic field

Basically I'm just trying to find the expression for the angular momentum of a particle of mass $m$ and charge $q$ in a dipole magnetic field. In cylindrical coordinates, ...
3
votes
0answers
208 views

Finding the terminal velocity of a magnet dropped in a solenoid

We have to find proportionality of the terminal velocity with the factors of the system: Plot: a small dipole(mass $m$) with dipole moment $\mu$ is dropped in a long solenoid (radius $r$, ...
3
votes
0answers
756 views

Effective mass in Spring-with-mass/mass system

Suppose you have a particle of mass $m$ fixed to a spring of mass $m_0$ that, in turn, is fixed to some wall. I'm trying to calculate the effective mass $m'$ that appears in the law of motion of the ...
3
votes
0answers
447 views

Shape of a string/chain/cable/rope/wire?

The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc ...
3
votes
0answers
125 views

Bandgap Spacing in Photonic Crystals

I am doing some self-study on photonics and have encountered the following question: We know that amorphous electronic crystals such as amorphous silicon have a bandgap. Can amorphous photonic ...
3
votes
0answers
101 views

The force exerted by a ~10 Tesla magnet on a C13 isotope?

How much force would a ~10 Tesla magnet exert on a weakly magnetic C13 isotope? If I made a molecule of diamond with $N$ C13 atoms, how large would $N$ need to be for me to pull on it with something ...
3
votes
0answers
455 views

Goldstone modes and Heisenberg model

The ideia is to show that, because of Goldstone modes, 2d systems are quite different from 3d ones. So, considering the Heisenberg model, I'll post here what I'm asked to and my current thoughts on ...
3
votes
0answers
172 views

Matter-wave interference from free falling cold atoms

and another exam question, this is about current research: Interference of matter waves has been studied using ultra-cold atoms. The phase of a matter wave for free-falling cold-atoms at time $t$ ...
3
votes
0answers
638 views

How do I derive the critical temperature for bose condensation in two dimensions?

In class we derived the 3D case, but there's a step I don't understand: $$ N = g \cdot {V \over (2 \pi \hbar)^3} \cdot \int\limits_{0}^{\infty}{1 \over{e^{\left( E_p \over{K_B T}\right)}-1}} d^3 p = ...
2
votes
0answers
52 views

S-Matrix Generating Functional (Problem 4.1 in Weinberg)

I'm currently working through Weinberg's QFT book, but I'm somewhat stuck at problem 4.1, which states: Define generating functionals for the S-matrix and its connected part: \begin{equation} ...
2
votes
0answers
56 views

How to calculate launch angle for tangentially launched satellites?

What is the value of theta for a satellite not falling back to the Earth if it is launched from the direction tangent to the surface of the Earth? I have found the escape velocity which is 11.18km/s, ...
2
votes
0answers
33 views

WKB approximation in two dimensions

Does anybody know how to implement the WKB approximation for the two-dimensional Schrodinger equation with a harmonic oscillator potential: $\frac{1}{2}\Biggl[-\biggl(\frac{\partial^2}{\partial ...
2
votes
0answers
59 views

Proof involving the fine-structure Hamiltonian of the Hydrogen atom

Given the perturbed Hamiltonian of the Hydrogen atom: $$ ...
2
votes
0answers
56 views

Proving that Measurement increases von Neumann entropy

Let $V$ be a finite dimensional complex inner product space. Let $\mathcal{M}$ be the classical sample space of measurement outcomes that may occur in a given experiment, and $M_\mu$, $\mu \in ...
2
votes
0answers
36 views

Laplacian in 4 spatial dimensions; 4th dimension warped

How can I prove the form of the Laplacian in four spatial dimensions, using the identification $y = y + 2\pi R$ for the fourth dimension and assuming the others as the usual Cartesian ones? I want to ...
2
votes
0answers
26 views

Normal modes of two wires fastened together

The problem is to find the normal frequencies of the system formed by two fastened wires of length L, and different mass per unit length. I already wrote the boundary conditions, but I need to know ...
2
votes
0answers
39 views

De-excitation and vibrational frequency

By utilising energetic beams of particles it is possible to set atomic nuclei into vibration. For a certain nucleus the subsequent de-excitation results in the emission of photons of energy $1$ $MeV$. ...
2
votes
0answers
39 views

Transformation Law for Covariant Derivative in $SU(2)$ Yang-Mills

In page 488 of Peskin and Schroeder, it is stated (emphasis mine): It is not difficult to check using (15.27) and (15.21) that, even for finite transformations, the covariant derivative has the ...