# 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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### 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 ...
1 vote
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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1 vote
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### 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, ...
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### 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 ...
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### 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 ...
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### 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/...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 $\vec{D},\ \vec{E}$...
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 ...