Skip to main content

Questions tagged [symmetry]

Symmetries play a big role in modern physics and have been a source of powerful tools and techniques for understanding theories and their dynamics. We say that something is symmetric if there is some transformation we can perform on that object that leaves some property unchanged. The set of symmetry transformations of an object forms a group, and the name of this group is used as the name of the symmetry of the object.

Filter by
Sorted by
Tagged with
0 votes
1 answer
51 views

Two contradictory derivations of Killing equation

In David Tongs lecture notes he derives the Killing equation by showing that the charge $Q=\xi_\mu \frac{\mathrm{d}x^\mu}{\mathrm{d}\tau}$ is conserved $$ 0=\frac{\mathrm{d}Q}{\mathrm{d}\tau}=\frac{\...
Silas's user avatar
  • 494
-2 votes
1 answer
80 views

Parity transformation of the $\pi^{0}\rightarrow\gamma\gamma$ process

I want to prove that the amplitude $$\mathcal{M}^{\mu\nu}=\epsilon^{\mu\nu\alpha\beta}q_{1\alpha}q_{2\beta}$$ is violating parity. Here $q_{i=1,2}$ are the external momenta of the photons. The total ...
Filippo's user avatar
  • 477
0 votes
1 answer
29 views

Understanding Symmetries and Invariances in Electrostatic Fields [closed]

I'm currently studying electrostatics and I'm having trouble understanding the concepts of symmetries and invariances of electrostatic fields. I understand the basic definitions of symmetry planes and ...
Boulahya Kaouthar's user avatar
1 vote
0 answers
15 views

Potential of Monolayer Graphene as a High-Precision Cutting Material

"I am exploring the use of monolayer graphene as a cutting material for high-precision applications. We know that graphene has exceptional mechanical properties, such as high strength and ...
Davi Diniz's user avatar
2 votes
2 answers
79 views

How does inserting an operator in the path integral change the equation of motion?

I am reading this review paper "Introduction to Generalized Global Symmetries in QFT and Particle Physics". In equation (2.43)-(2.47), the paper tried to prove that when $$U_g(\Sigma_2)=\exp\...
gshxd's user avatar
  • 133
3 votes
1 answer
40 views

Using particle-hole symmetry of the Hubbard model to study the model at different densities

In Condensed Matter Field Theory by Altland and Simons, they state that the Hubbard Hamiltonian $$ H = \sum_{\text{nearest neighbors } ij \text{ and spin } \sigma} a^\dagger_{i\sigma} a_{j\sigma} + U \...
zeroknowledgeprover's user avatar
1 vote
2 answers
131 views

Is the FRW metric, based on spatial homogeneity and isotropy, rotationally and translationally invariant? If so, how?

The spatial part of the Minkowski metric, written in the Cartesian coordinates, $$d\vec{ x}^2=dx^2+dy^2+dz^2,$$ is invariant under spatial translations: $\vec{x}\to \vec{x}+\vec{a}$, where $\vec{a}$ ...
Solidification's user avatar
1 vote
1 answer
58 views

Designing a thought experiment on Noether's Theorem [closed]

By Noether's theorem, in classical physics, conservation of total momentum of a system is result of invariance of physical evolution by translation. So logic says "if" there exists closed ...
moshtaba's user avatar
  • 1,409
3 votes
0 answers
69 views

Does all symmetry breaking have corresponding unitary group?

In high energy physics. Symmetry breaking like electroweak's has corresponding $SU(2)\times U(1)$ unitary gauge group broken down to $U(1)$. Does it mean all kinds of symmetry breaking (even low ...
Jtl's user avatar
  • 425
-3 votes
1 answer
78 views

Probabilistic behavior of quantum mechanics [closed]

In a hypothetical scenario, if I were to measure the quantum spin of an electron and it showed "up," and then I traveled back in time without changing the initial conditions, would measuring ...
Vishnu's user avatar
  • 15
0 votes
0 answers
24 views

Embedding diagram of $\phi=\mathrm{constant}$ surface in cylindrically symmetric spacetime

I'm trying to generate an embedding diagram for the $\phi=\mathrm{constant}$ hypersurface in a cylindrically symmetric spacetime. I think I'm supposed to start with $$A(p,z)dp^2+A(p,z)dz^2=dw^2+dp^2+...
user345249's user avatar
0 votes
1 answer
47 views

Doubts in circuit analysis [closed]

I am really confused here how is the potential at O found? Resistance is equal at all resistors this is an illustration in my book, they have not explained why voltage at O is 50V, just stated that ...
Anton Bert's user avatar
1 vote
2 answers
105 views

Checks of anomaly cancellation

In a textbook I read that if $G$ is a global symmetry of the classical Lagrangian, then one has to check $G\times H^2$ anomalies, where $H$ is one of the SM gauge groups. For example, when $G$ refers ...
Fern's user avatar
  • 51
0 votes
0 answers
15 views

Ward identity for special conformal transformation in d dimensions

I am reading CFT from the yellow book ( "Conformal Field Theory" by Francesco, Mathieu, Sénéchal ). In section 4.3.2, they calculate three Ward identities corresponding to (i) translation ...
baba26's user avatar
  • 513
0 votes
0 answers
10 views

Is axial symmetry the same as transverse isometry?

I was reading this paper ArXiv link And trying to picture everytime he mentioned "transverse isotropic plate" I began to imagine something that is equal on all directions on a plane, but not ...
Elkin Montoya's user avatar
0 votes
0 answers
13 views

Symmertry of $R$-tensor of Stark Effect in diamond structure

Currently, I am studying the effects of electric fields on color centers in diamonds. However, I have encountered a problem: when addressing the Stark effect caused by the electric field, I use the R ...
Annihilation's user avatar
0 votes
1 answer
48 views

Relationship Between Ground State Wavefunctions' Amplitudes Under Discrete Symmetry Operations

$\newcommand{\ket}[1]{\left|#1\right\rangle}$ Given a Hamiltonian $\hat{H}$ and a discrete symmetry $\hat{T}$, it's known that $\hat{T}\ket{\psi_{GS}}$, where $\ket{\psi_{GS}}=\sum_\sigma \psi_{GS}(\...
Andy Liu's user avatar
2 votes
1 answer
59 views

Derivation of Noether Current in Condensed Matter Field Theory by Altland and Simons

In Section 1.6 of Condensed Matter Field Theory by Altland and Simons, they prove Noether's theorem. In order to do so, they consider an infinitesimal transformation of the coordinates and the field: $...
zeroknowledgeprover's user avatar
1 vote
1 answer
86 views

Symmetrizing of projectors with identical particles

I am dealing with systems of $N$ identical particles in quantum mechanics. The tensor product state space is : $V^{\otimes N}$. (in the question is use the term symmetrized to designate either ...
cmatteo's user avatar
  • 254
0 votes
0 answers
32 views

DMI as a Superexchange?

Superexchnage interaction is an indirect exchange interaction between two magnetic ions; Anderson proposed a model that says the origin of this type of exchange is due to the arrangement of Molecular ...
Shubhay Dikkar's user avatar
2 votes
1 answer
68 views

How does a $\mu_R^-/\mu_L^+$ decay?

While studying SM, I was taught that weak force bosons $V=\{W^\pm,Z^0\}$ do not interact with right/left-chiral fermions/antifermions. For this reason, we cannot observe right-handed neutrinos (if ...
A.M.M Elsayed 马克's user avatar
11 votes
1 answer
139 views

Is there a conceptual inverse of anomalies i.e. a notion of quantum enhancement of symmetries?

Anomalies usually occur when a classical symmetry ceases to be a symmetry of the theory when quantized. Are there quantum systems with certain symmetries which cease to exist when you take classical ...
Sanjana's user avatar
  • 785
-1 votes
1 answer
62 views

Translational invariance $\neq $ Galilean invariance?

I have the impression that some literature say that Galilean invariance is broken by a uniform lattice. That is, although a uniform lattice like a tight binding model is translationally invariant, it ...
poisson's user avatar
  • 1,957
2 votes
0 answers
50 views

Invariance under Lorentz transformations but not translations?

I've read here that it's not possible to construct a field theory which is invariant under boosts but not invariant under rotations. The reason is essentially that boosts aren't closed under ...
WillHallas's user avatar
6 votes
1 answer
158 views

Radial reparametrization ansatz in Schwarzschild metric derivation

The standard derivation of Schwarzschild solution (and Birkhoff's theorem) seem to begin with the most general spherically symmetric static metric $$ds^2 = -U(\rho) dt^2 + V(\rho) d\rho^2 + W(\rho) \...
UnkemptPanda's user avatar
2 votes
1 answer
48 views

Does Noether's theorem apply to a strict on-shell symmetry of the action that holds on every integration region?

I've worked through different proofs of Noether's theorem and read various posts about it on this site. Some important takeaways, among others from this and this post by Qmechanic were Every off-...
WillHallas's user avatar
0 votes
0 answers
42 views

Is there a deeper relationship between symmetry and gravitational potential comparing Newton's and Einstein's gravity?

In this question, see Why is general relativity in (2+1) dimensions different from cylindrical systems in (3+1) dimensional GR?, it is mentioned "The gravitational potential Φ of an infinite rod ...
timm's user avatar
  • 1,589
2 votes
0 answers
98 views

Emergence of Dirac Cones: Triangular Lattice vs. Honeycomb Lattice

I'm reading the paper 'Honeycomb Lattice Potentials and Dirac Points' by Fefferman&Weinstein. To my understanding they claim that the existence of Dirac Cones at K/K' points is entirely determined ...
Julian's user avatar
  • 21
0 votes
2 answers
81 views

Is von Neumann entropy symmetric? [closed]

In a multiparty system, Shannon entropy is symmetric with respect to exchange of two parties. Is this also true for von Neumann entropy in case of a multiparty density matrix? If yes, is there any ...
asu's user avatar
  • 11
2 votes
2 answers
100 views

Variation of the Lagrangian expressed as a time derivative of a function

In chapter 4.5 of Jakob Schwichtenberg's Physics from Symmetry, he expresses the variation of the Lagrangian $L = L\left ( q, \dot{q}, t \right )$ with respect to the generalized coordinate $q$ as $$\...
tugboat2's user avatar
4 votes
3 answers
669 views

What is the proof that the Schwarzschild metric is not static inside the horizon?

In Lecture Notes on General Relativity, Sean M. Carroll shows that the Schwarzschild metric is not only stationary but also static (Chapter 7, page 169, Eq. 7.20 and following interpretation). On the ...
JanG's user avatar
  • 1,948
1 vote
2 answers
82 views

Calculating equivalent resistance of a beautifully "symmetric" circuit [closed]

In the given circuit, we have to find the resistances between A and B. I like to solve such problems by first finding out points which are equipotential, as resistors between such points are ...
Bongo Man's user avatar
  • 131
0 votes
1 answer
103 views

Birkhoff's theorem and Schwarzschild vacuum solution [duplicate]

Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat, but the well-known Schwarzschild solution satisfies these ...
JanG's user avatar
  • 1,948
1 vote
1 answer
62 views

Symmetry transformation exact meaning

In whatever text/review I happen to come across (like for example From Noether’s Theorem to Bremsstrahlung: A pedagogical introduction to Large gauge transformations and Classical soft theorems, ...
schris38's user avatar
  • 3,982
30 votes
5 answers
14k views

How can a point source emit spherical EM waves when they are forbidden by Maxwell's equations?

I know that there exist plane wave solutions to the Maxwell equations in free space, and I tried solving them for a spherical wave emanating from a point but could find no solution consistent with the ...
Thanos's user avatar
  • 419
0 votes
1 answer
48 views

Finding the Noether current

I'm currently reading "QFT for the gifted Amateur by Lancaster and Blundell, and in a lot of the problems I'm a bit unsure of how to do them, an example asked "Consider a system ...
Morty Levinson's user avatar
0 votes
0 answers
19 views

How to determine refelection symmetry of molecular term in relativistic (spin-orbit) molecular term?

It is quite clear and well-described how to determine the molecular term of diatomic molecule from interacting atoms (including parity and reflection symmetry): https://chem.libretexts.org/Bookshelves/...
Adam 's user avatar
0 votes
0 answers
30 views

Why is charge parity (eigenvalue of $\hat{C}$) conserved?

Looking at processes with neutral initial and final state, for example $$e^+e^- \rightarrow \gamma \gamma$$ we know that charge parity (eigenvalue of charge conjugation operator $\hat{C}$) is ...
Jahi02's user avatar
  • 255
1 vote
1 answer
93 views

How is Noether’s theorem actually applied?

Noether’s theorem roughly states that the existence of a symmetry group for a given system implies a conservation law for that system. All well and good, except that I’m shaky on exactly how you ...
controlgroup's user avatar
0 votes
0 answers
28 views

Role of particle number conservation for SPT order

It is shown in https://arxiv.org/abs/1111.6341, that non interacting SPT phases of fermions are at least protected by U(1) symmetry (a.k.a. particle number conservation). I wondered if this result ...
Shadow's user avatar
  • 83
0 votes
1 answer
46 views

Is color charge internal symmetry or global symmetry?

I was told the color charge in the standard model could not be observed directly. This sounded like the gauge field $\vec A$ in the electromagnetism. However, it is a discrete charge and does have ...
ShoutOutAndCalculate's user avatar
1 vote
1 answer
183 views

Why does a group of charges with spherical symmetry, where each oscillates radially while retaining spherical symmetry, not radiate? [duplicate]

I am thinking about the problem, "Why does a group of charges with spherical symmetry, where each oscillates radially while retaining spherical symmetry, not radiate?" I figured out that ...
KingWangZZang's user avatar
0 votes
2 answers
54 views

Significance of charge $U(1)$ transformation looking like time evolution

In QM, the "charge" observable corresponds to representations in which the group transformation advances the phase of the state. Similarly, time evolution via the Schrodinger equation also ...
HoosierDaddy's user avatar
0 votes
0 answers
30 views

Noether's theorem for supersymmetry [duplicate]

I know that Noether's theorem states that all symmetries of the universe correspond to some conservation law. If supersymmetry were true, would there be a new conservation law? In other words, does ...
mathman's user avatar
0 votes
0 answers
26 views

How does spontaneous supersymmetry breaking lead to different masses between superpartners?

For the past few days I've been studying supersymmetric quantum mechanics. My main sources that I use are David Tong's lecture notes on supersymmetric quantum mechanics, as well as Edward Witten's ...
luki luk's user avatar
0 votes
1 answer
21 views

Can we treat the entire mass of the spheroid as being concentrated at its center?

I know that to find the gravitational force between two objects, if either of them is a sphere, we can assume its mass to be concentrated at its center and use the formula for gravitational forces for ...
Peter swift's user avatar
2 votes
0 answers
50 views

Energy of a spherical shell

System: spherical shell with surface density. Objective: calculate potential energy. I found energy through potential. Next, I found the formula for energy through the field, which gives two ...
neo's user avatar
  • 21
1 vote
1 answer
51 views

Difference in definition of conserved current in Quantum Field Theory

In David Tong Lecture Notes (page 14), it is written that Proof of Noether's Theorem: We'll prove the theorem by working infinitesimally. We may always do this if we have a continuous symmetry. We ...
darkphysics's user avatar
0 votes
1 answer
60 views

Why the dielectric permitivity matrix of lossless media is symmetric?

I am studying optics and I met a strange statement in the section 2.3.4 (page 34) of Fundamentals of Nonlinear Optics by Peter E. Powers and Joseph W. Haus. The relationship between $\vec{D},\ \vec{E}$...
Hsu Bill's user avatar
  • 388
1 vote
0 answers
39 views

Non-invertible symmetries: Half gauging and 't Hooft lines

In (2.27) of https://arxiv.org/abs/2205.05086, when performing a gauge transformation of the background gauge field $B \to B +d \Lambda $, the 't Hooft line $H(\gamma)$ transforms as \begin{equation} ...
superyangmills's user avatar

1
2 3 4 5
66