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.

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Forms of interaction between two spins

I am learning the principles of nuclear magnetic resonance, and came across the interaction between two Hydrogen nuclear spins, which affects the relaxation properties of materials like water in NMR. ...
night cat's user avatar
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$xy$-symmetry of the electric potential: Charged sphere at an external uniform electric field

Griffiths Introduction to Electrodynamics problem 3.21 Find the potential outside a charged metal sphere of charge $Q$ and radius $R$, placed in an otherwise uniform electric field $E_0\hat{z}$. The ...
Leo's user avatar
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Is there Noether charge for any continuity equation? [duplicate]

Based on Noether theorem, if under infinitesimal coordinates transformation $$x^{\mu}\longrightarrow \overline{x}^\mu=x^\mu+\epsilon^i\lambda^\mu_i(x)$$ where the range of the index i is at this ...
Sancol.'s user avatar
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How to choses coordinate systems and change between them? [closed]

I understand that when choosing a system for the problem that interests me I need to consider all the things that effect what I want to calculate and try to pick the thing that fits my interests the ...
lodo's user avatar
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A question from S. Weinberg's book (Sec. 2.7)

S. Weinberg in his book "The quantum theory of fields" page 82 says: the elements $T,\bar{T}$, etc, of the symmetry group may be represented on the physical Hilbert space by unitary ...
Mahtab's user avatar
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Conserved current from a symmetry

Good morning. I was reading Tong's Quantum Field Theory course and got stuck on a somewhat stupid step. Essentially, considering the Lagrangian density $$ L = - F_{\mu \nu}F^{\mu \nu} + i \bar{\psi} \...
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Which Potentials lead to Kepler's second Law?

Which type of potentials lead to Kepler's second law "same area in same time"? $$dA=\frac{1}{2} \vec{r} \times \vec{dr}.$$ $$\frac{dA}{dt}=c=\vec{r} \times \frac{\vec{dr}}{dt}=\vec{r} \...
16π Cent's user avatar
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Lie group symmetry in Weinberg's QFT book

In Weinberg's QFT volume 1, section 2.2 and appendix 2.B discuss the Lie group symmetry in quantum mechanics and projective representation. In particular, it's shown in the appendix 2.B how a ...
liyiontheway's user avatar
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Intuition for the interior Killing vector fields in Schwarzschild?

The Schwarzschild metric represents a stationary (and static), spherically-symmetric, spacetime. These characteristics are manifested by the four Killing vector fields: one for time translation and ...
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Do supertranslations act in a physically nontrivial way?

I'm currently reading arXiv: 1703.05448 [hep-th]. In this question, I'm interested in a statement made on page 67 of the pdf (76 of the printed book, if you prefer to check in it). There, the author ...
Níckolas Alves's user avatar
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Proving spherical harmonics' spherical symmetry and invariance under rotations?

I was told in a lecture the following relationship, where $Y_{\ell}^m$ are the spherical harmonics and the eigenfunctions of the two following operators: $$ L^2 Y_{\ell}^m = \ell(\ell + 1) \hbar^2 Y_{...
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What is the allowed operator in a global/ local theory?

While I'm reading Hong Liu's notes, it says: Now we have introduced two theories: (a)$$\mathcal{L}=-\frac{1}{g^2}Tr[\frac{1}{2}(\partial \Phi )^2+\frac{1}{4}\Phi^4]$$ (b)$$\mathcal{L}=\frac{1}{g^2_{...
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What isn't the metric invariant under translation with killing vectors?

I am learning about Killing Vectors in GR class, and I'm testing my knowledge of them as a start with the Minkowski metric. I used the simple 2d Minkowski metric: $$ds^2 = -dt^2 + dx^2$$ and got 3 ...
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Does the divergence theorem imply an underlying symmetry?

The divergence theorem connects the flux (through surface) and divergence (in a volume) for any vector field. This theorem expresses continuity. It isn't clear (to me) whether there is a conserved ...
AppliedAcademic's user avatar
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On the Wigner symmetry representation theorem

Wigner symmetry representation theorem tells that if $\mathcal{S}:\mathbb{P}\mathcal{H}\to \mathbb{P}\mathcal{H}$ is a symmetry, then $\mathcal{S}[\Psi]=[\hat{U}\Psi]$ where $\hat{U}:\mathcal{H}\to \...
Mahtab's user avatar
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Possible divergence of susceptibility without spontaneous symmetry breaking?

In the article Strange Metals as Ersatz Fermi Liquids , the authors mentioned in the left bottom paragraph on page 4 that Furthermore the diverging susceptibility of an order parameter at a quantum ...
Black Monolith's user avatar
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Problem with the line of reasoning used by Feynman in a proof that the force felt by a point outside the earth can be approximated by a point mass [closed]

I was following the proof in the lecture 13 of Feynman Volume 1 where he proves that the force produced by the earth on a point outside or on the surface of it is equal to force produced by a point ...
User13114's user avatar
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Perturbation Theory with no symmetry breaking?

I was learing about group theory in QM and stable about symmetry breaking. I find it very interesting and search some stuff and even looked on wikipedia and found this: https://en.wikipedia.org/wiki/...
Alexandru Chirvasa's user avatar
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Does the Lagrangian being invariant under substitution of variables imply a conserved quantity?

Consider the following Lagrangian: $$ \mathcal{L} = \frac{Ma^2\dot\theta^2}{6} +\frac{1}{2}ma^2\left(4\dot\theta^2 + \dot\phi^2 + 4\dot\theta\dot\phi\cos(\theta - \phi) \right) - \frac{a^2k}{2}\left( ...
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How to tell whether Hamiltonian has rotational invariance? Conservation of angular momentum?

If a system contains isotropic exchange interaction and uniaxial anisotropy in the $z$-direction, does this Hamiltonian satisfy rotational invariance of the $z$-direction so that the spin angular ...
Xin's user avatar
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6 votes
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Can we define topological order in the context of QFT?

Topological order is defined to be a phase that has ground state degeneracy (GSD) not described by the Landau SSB paradigm but exhibits some Long Range Entanglement property. Mathematically, it is ...
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Confused about spherically symmetric spacetimes

I'm following Schutz's General Relativity book and I am confused about his description and derivations of a spherically symmetric spacetime. I searched online and found that using Killing vectors is a ...
Kiwi breeder's user avatar
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Understanding symmetry arguments to derive the coupling coefficients between modes of a unit cell in a periodic system

I am reading a paper that derives the form of the Bloch Hamiltonian using the symmetry arguments. Let $D(k)$ be the Bloch Hamiltonian, where $k$ is the wavenumber. The part that I am trying to ...
Mohit Kumar's user avatar
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Srednicki 36.5 symmetry question

This is from the intro to a problem 36.5 in Srednicki and not part of the problem itself. I am having trouble proving that $$\mathcal{L}=i\psi_j^\dagger\sigma^\mu\partial_\mu\psi_j$$ Has $U(N)$ ...
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Does the Hamiltonian formalism yield more Noether charges than the Lagrangian formalism?

In Lagrangian formalism, we consider point transformations $Q_i=Q_i(q,t)$ because the Euler-Lagrange equation is covariant only under these transformations. Point transformations do not explicitly ...
watahoo's user avatar
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Can you assume the energy-momentum tensor is symmetric if you only impose Lorentz symmetry?

The proof showing that the energy-momentum tensor is symmetric uses the fact that $\partial_\nu T^{\mu\nu}=0$ due to translation symmetry, the definition of the conserved current and that $\partial_\...
Chris G's user avatar
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What symmetry present in a low energy theory is broken or not exact at high energies?

The opposite is quite common such as EWSB, SUSY or GUT. Is there any example where a certain symmetry emerges from a low energy effective theory but is not present in the high energy theory?
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What are Supertranslations and Superrotations in General relativity, and how does it inform us about a detector at null infinity?

How did I get here? While drafting my question, I found this very similar question on our site. Three days ago, I happened upon the concept of supertranslations and superrotations in General ...
Kevin Njokom's user avatar
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Hamiltonians with collective quantum spins and their ground states

This feels like it could be a undergrad/grad-school quantum mechanics course level problem, or potentially something pretty interesting. I'd be happy with either answer, but I don't know which one is ...
Jun_Gitef17's user avatar
7 votes
1 answer
202 views

Gauge theories, boundaries and Wilson lines

My understanding of Wilson loops Let's work with classical electromagnetism. The 4-potential $A_\mu$ determines the electric and magnetic fields, which are the physical entities responsible for the ...
P. C. Spaniel's user avatar
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Confusion regarding scale symmetry for certain charge configurations

I had a question on symmetry operations that exactly resembles this post. The selected answer there mentions the required symmetry operation to be scale symmetry, and says: An infinite plate looks ...
archthegreat's user avatar
2 votes
1 answer
199 views

What's the meaning of this path integral measure?

I don't understand the meaning of following path integral measure $$ \frac{[df]}{U(1)} $$ What is the difference between $[df]$ and $[df]/U(1)$? A naive idea is the latter measure is more physical ...
runaway's user avatar
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2 votes
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Approximating the $U(1)$ Schwinger model with a $\mathbb{Z}_2$ symmetry

The Schwinger model or $(\text{QED})_2$ essentially is quantum electrodynamics defined in $1 + 1$ spacetime dimensions. In https://arxiv.org/abs/2305.02361 they use the Hamiltonian formulation to ...
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Confusion about the derivation of stress tensor OPE from Ward Identity

I apologize for any difficulty in expressing my review. Allow me to briefly summarize the material and then pose my question. Review In David Tong's string lecture note, he derives the OPE between ...
Steven Chang's user avatar
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Do all solutions to the Dirac equation transform as spinors?

Usually, the Dirac equation is introduced as the equation $D \psi = 0$, which is form invariant under Lorentz transformations ($\Lambda$), when $\psi$ transforms as a spinor $\psi' \to S(\Lambda) \psi$...
Sidd's user avatar
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Canonical electromagnetic stress-energy-momentum tensor

I have canonical electromagnetic stress-energy-momentum tensor defined as: $T_{\mu\nu}=\frac{1}{4}\eta^{\mu\nu}F_{\alpha\beta}F^{\alpha\beta}-F^{\mu\lambda}F^{\nu}_{\,\,\lambda}-F^{\mu\lambda}\...
Lilla_mu's user avatar
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Why do we expect isometries of bulk side to be equivalent to symmetries of the CFT?

One can clearly see that the AdS bulk isometries form the $SO(d,2)$ symmetry of the $d$ dimensional CFT explicitly. Why does this occur: why don't the isometries of the spacetimes match up or the ...
Sanjana's user avatar
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Does truly accidental degeneracies exist anywhere in quantum systems?

I was wondering whether there are instances of truly accidental degeneracy in physics i.e., degeneracies that cannot be linked with some symmetry of the system/Hamiltonian. I have the following ...
Solidification's user avatar
1 vote
1 answer
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Energy-Momentum tensor in Classical Mechanics

I can compute Energy-momentum tensor in classical field theory using Noether's theorem and translation invariance of action, but I think I can't exactly calculate how to calculate same thing in ...
Mahammad Yusifov's user avatar
15 votes
3 answers
3k views

Why do fields have to form a representation of the Lorentz group?

It is often claimed in quantum field theory texts that to have a sensible Lorentz invariant theory, the fields introduced must be in representations of the Lorentz group. This fact has always seemed ...
Leuca Patmore's user avatar
1 vote
1 answer
51 views

Do the WI coupling constants change sign under $C$?

I am trying to understand discrete symmetries in the SM, and I have some troubles in understanding why the CC interaction violates CP. In my (badly written) notes it's said that, taken two fermonic ...
Filippo's user avatar
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Stationary, static and strictly stationary/static?

Consider spacetimes which are asymptotically flat at null infinity. How to explicitly show that there exists a hyper-surface orthogonal killing vector field $k^{a}$ that is time-like everywhere in ...
John 's user avatar
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What is the Noether stress-energy tensor?

The goal is to find the formula for the stress-energy tensor, of mass-energy field. The Poincare group's algebra generates it with 3+3+4 generators, the first 6 or the continuous Lorentz subgroup (Let'...
user192234's user avatar
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2 answers
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Question on Peskin & Schroeder's QFT: Noether's Theorem; finding conserved currents

So, I am trying to learn how to find conserved currents using what I see in P&S's "Intro to QFT"; sec.2.2 pg.17-18. Particularly, I am working through the example in the text for the ...
Albertus Magnus's user avatar
1 vote
2 answers
141 views

Before spontaneous symmetry breaking, what is the difference between the fermion generations?

Before spontaneous symmetry breaking (SSB), all fermions have the same mass (0). Across the 3 different fermion generations, all the (left) quarks doublets have the same weak isospin, and all the up ...
TrentKent6's user avatar
7 votes
5 answers
713 views

Why do molecules lack the inversion symmetry of the full molecular Hamiltonian?

The nonrelativistic molecular Hamiltonian has inversion symmetry, since the kinetic energy operator and the Coulomb operator have inversion symmetry, $$\begin{aligned} \hat p_i^2&\stackrel{i}{\...
Hans Wurst's user avatar
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2 votes
1 answer
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Doubts about Noether's theorem derivation

Assume you have an action: $S[q] = \int L(q, \dot q, t)$ (i.e $q$ is a function of time). (1) Then you do a transformation on $q(t)$ such as $\sigma(q(t), a)$ where $a$ is infinetisemal and this ...
Giorgi Lagidze's user avatar
2 votes
1 answer
51 views

Computing the Free Parafermion Spectrum

In Fendley's paper on Free Parafermion (https://arxiv.org/abs/1310.6049), Fendley used some operator techniques to show that $$Q_{2 L}\left(\epsilon_k^n\right)=0$$ which is the formal derivation of ...
ZHENGYAO HUANG's user avatar
0 votes
1 answer
88 views

What is the (non-broken) Peccei-Quinn symmetry?

In the references I read, it's always said that the Peccei-Quinn (PQ) symmetry is a $U(1)$ symmetry, and the PQ Lagrangian has a potential term that, for a certain temperature, assumes a mexican-hat ...
Mauro Giliberti's user avatar
3 votes
1 answer
66 views

Proof that a scalar field invariant under rotations only depends on norm

Let $f: \mathbb{R}^3 \rightarrow \mathbb{R}$ be a real valued scalar field and $\mathbf{r}\in\mathbb{R}^3$ a vector with $r = \sqrt{\mathbf{r}\cdot\mathbf{r} }$ its norm. Let's say that $f$ is ...
Pere Rosselló's user avatar

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