# Questions tagged [symmetry]

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 form a group, and the name of this group is used as the name of the symmetry of the object.

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### How to correctly use Gauss Law? Why is it used the way it is? [closed]

Gauss Law $$\oint \vec E . d \vec A = \frac{Q_{enclosed}}{\epsilon _○}$$ From this question, Gauss Law is more fundamental than Coulomb's Law. This seems counter intuitive to me when it comes to ...
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### Why $|H_1(\Sigma,\mathbb{Z}_N)|$ can be interpreted as an 1+1d $\mathbb{Z}_2$ gauge theory?

I am reading the article https://arxiv.org/abs/2204.02407, and I am struggling with the definition of a condensation defect, which is given by \begin{align} S(\Sigma)=\frac{1}{\sqrt{|H_1(\Sigma,\...
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### A question about space inversion symmetry of parity in a rotated disk

In a rotated disk (say, Faraday disk), is the space inversion symmetry of parity still preserved?
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### Construction of an $N$ electron orbital and spin state

Consider a system of $N$ electrons. Their Hilbert space is the antisymmetric subspace of $\mathcal H = \mathcal H_e^{\otimes N}$, where $\mathcal H_e \cong L^2(\mathbb R^3)\otimes \mathbb C^2$ is the ...
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### Symmetric and Antisymmetric states for 3 Quarks

I think we suppose to have 27 states if we are talking about three quarks. can anyone explain to me how to identify the symmetric states and antisymmetric ones ? or even a keyword in which I use it to ...
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### Electron momentum in a one-dimensional lattice and conservation issue

A one-dimensional lattice is a periodic array of atoms or ions where any two adjacent ions are separated by a fixed distance, the lattice spacing $a$. The Hamiltonian of an electron moving in this ...
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### Why can't we gauge the Lorentz group? (Or can we?)

One of the (many different, somewhat independent) routes to gauge theory is to start from a global symmetry of some kind and "gauge" it, which involves promoting it to a local symmetry and ...
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### Symmetry Factor and Wicks Theorem

I have a problem with a particular kind of exercise. The question is: Consider $\phi^4$-theory with $\mathcal{L}_\text{int}=-\frac{\lambda}{4!}\phi^4$. Give the symmetry factors of the diagram and ...
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### Can you prove the possibility to rewrite any lorentz invariant equation as the component of a 4-tensor?

When studying special relativity, there is usually a point where 4-tensors get introduced. Since all of physics equations are supposed to be lorentz-invariant, it is assumed that these equations are ...
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### All Michelson-Morley experiments have only been done in non-inertial conditions. Does special relativity apply or not?

As far as I know not a single Michelson-Morley experiment has been done in non-inertial conditions. Shouldn't it be general relativity that applies to Michelson-Morley experiments done so far?
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### Some books write $V(\vec{r})$ instead of $V(r)$ as a notation for the electric potential, so which one is right? [closed]

Some books write $V(\vec{r})$ instead of $V(r)$ as a notation for the electric potential, so can the electric potential depends also on the direction?
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### What does it mean that the standard model Lagrangian obeys a symmetry?

It is said that the standard model has a SU(3) $\times$ SU(2) $\times$ U(1) symmetry. Sometimes I see that the precise symmetry is slightly different. Which one is the precise one? And in what sense ...
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### For what reasons of symmetry does the magnetic field inside an infinite solenoid not have an azimuthal component?

When deriving the magnetic field inside of an infinitely long solenoid carrying a stationary current, it's useful to take into consideration the symmetries of the problem, in order to understand which ...
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### How check the c4v symmetry in a hamiltonian?without using geometry

In the 2D square ssh model, how to check that the Hamiltonian does not change under c4v symmetry. Based on the square geometry of this model, it is possible to realize the existence of c4v symmetry, ...
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### Algebra equation for rank-3 tensor

Suppose I work in $4$ dimensions. I have an algebraic equation in the following form, which contains a rank-3 tensor $X ^{\alpha \lambda \mu }$ \begin{equation} X ^{\alpha \lambda \mu }\eta ^{\beta \...
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### Why is it not Pin(1,3) or Pin(3,1) in condensed matter physics?

In electron systems (or condensed matter physics), it is well known that $T^2=-1$ and $M^2=-1$, where $T$ and $M$ are time reversal and reflection along some axis. But in general, the symmetry of ...
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### Static spacetime and metric invariance

I'm studying General Relativity using Ray D'Inverno's book "Introducing Einstein's relativity". I don't understand what the author writes in paragraph 14.3 ("Static solutions") ...
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### Isotropy of space doubts

From the following image, why do we still call it isotropic? if the density at A and B differ, I don't think it's enough to call it isotropic. In my opinion, material is only isotropic if when we ...
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### Doubts about isotrophy and homogeneity of space

From the following answer, we note that space is isotropic if everything (force, amount of things, separation by distance, e.t.c) is the same in every direction. To call a space isotropic, it shouldn'...
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### What is the gravity in the center of Earth?

Let's suppose the earth is perfect sphere and let's ignore its rotation and movement. What would happen if i would be in the center of the earth? Would the gravity be zero in any direction so i wouldn'...
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### Antisymmetrization of the electronic wave function

I'm studying systems of many electrons (for Theoretical Quantum Chemistry) from Landau, Quantum Mechanics (non-relativistic theory), chapters 61, 62, and 63. I wanted to ask for good references to ...
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### Why does time-translational symmetry imply that energy (and not something else) is conserved?

I'm trying to understand Noether's theorem from an intuitive perspective. I know that time-translational symmetry implies the conservation of energy. Is it possible to convince oneself that time-...
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Due to the mass difference between the $u$-quark and the $d$-quark, SU(2) isospin symmetry is only an approximate symmetry (even in a universe devoid of weak and EM interactions). This suggests to me ...