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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Why is quark flavor just a SU(N) group?

In the standard model one has U(1) for electromagnetism, SU(2) for the weak sector and SU(3) for the color sector. One could say that in the quark part of the fermions, there are $$ ...
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34 views

A Question about a $U(1)_{B-L}$

I know I can write the QCD lagrangian like this: $$ \mathcal{L} = (i\bar{q}_{R} \gamma_{\mu}\partial_{\mu} {q}_{R} + i\bar{q}_{L}\gamma_{\mu}\partial_{\mu} {q}_{L}) + \text{other terms} $$ When ...
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0answers
36 views

What is the relationship between local and global symmetries? [on hold]

A global symmetry has a few different meanings. The obvious one is that for $g = e^{-i\theta}$ if $\theta$ is contant in space then a field $\phi$ transforms $\phi' = e^{-i\theta}\phi$ so that ...
-1
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1answer
49 views

Understanding standard model and symmetry

I just want to know whether my understanding regarding standard model and symmetry is correct or utter nonsense. The standard model is the (yet incomplete) Lagrangian of the universe. The ...
2
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0answers
69 views

Analyzing the free-particle kernel [closed]

I recently began studying the theory of path integrals from the book by Feynman and Hibbs. The Problem $3.6$ asks to give an argument to show that $F(t_b,t_a)$ depends only on $t_b-t_a$. ...
3
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104 views

Physical difference between gauge symmetries and global symmetries

There are plenty of well-answered questions on Physics SE about the mathematical differences between gauge symmetries and global symmetries, such as this question. However I would like to understand ...
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0answers
28 views

Is there a Symmetry-Topology duality? [closed]

Both symmetry breaking and topology "create" information within the Universe. It seems that topology causally affects symmetry and symmetry causally affects topology. Can the two concepts co-exist as ...
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1answer
42 views

Notations for high symmetry points in the 1st Brillouin zone

I am trying to understand how I should interpret the letters like Г,K,M,T etc., that are usually there in the electronic band structure diagrams. So, let's assume we have graphene with its hexagonal ...
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0answers
29 views

Antiunitary operators in the tenfold way

In the classification of free fermion systems in condensed matter, physicists usually divide the systems into ten symmetry classes, first discovered by Altland and Zirnbauer. In their classification, ...
3
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2answers
27 views

Standard-model flavor symmetry

If we consider the chiral Lagrangian after the spontaneous symmetry breaking, we have got fermion masses and Yukawa couplings to the physical Higgs boson. So it follows global symmetries in flavor ...
3
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0answers
134 views

Are symmetries of a degenerate ground-state manifold always broken?

If a Hamiltonian has a global symmetry and a degenerate ground state, then in the thermodynamic limit, the ground states $| \psi \rangle$ that are eigenstates of the symmetry operator typically become ...
2
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0answers
31 views

Kitaev chaing, time reversel symmetry, particle hole symmetry

I was wondering if the Kitaev chain has time reversal symmetry. I think it probably doesn't because by staking Kitaev chains it is possible to create a so called Chern insulator with propagating ...
0
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1answer
32 views

Inversion symmetry points of graphene

I have question about graphene. When you have the graphene lattice two types of atoms can be distinguished, let's call them type A and B.You can draw a unit cell that has the shape of a ...
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1answer
43 views

What are the assumptions behind the Lagrangian derivation of energy?

What are the assumptions behind the Lagrangian derivation of energy? I understand that we're searching for a function $L$ that describes a set of physics so that solving the energy minimization ...
1
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1answer
41 views

Crossing Symmetry in Bhabha scattering and Moller scattering

Given the amplitude for a particular process, it may be possible to obtain the amplitude for another similar process by a so called crossing symmetry. I know there is a $s \leftrightarrow u$ crossing ...
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0answers
24 views

Lorentz invariance & Noether theorem of classical ED

I want to check invariance of the action under Lorentz boosts for classical electrodynamics. The action is $$S = \int \mbox{d}^4x F_{\alpha \beta} F^{\alpha \beta} $$ I assumed that the fields ...
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0answers
12 views

Effect symmetry on points in momentum space

I have to study some material for a condensed matter physics course and cam across a passage that I don't understand. "In momentum space time reversal symmetry and particle hole symmetry only have ...
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0answers
17 views

effect of inversion symmetry on the bandstructure

I have a very general question, but I hope that someone can answer it. Can someone describe what the effect of inversion symmetry is on the bandstructure. (Or is there not a general effect?). ...
4
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1answer
78 views

What does it mean for a topological phase to be “symmetry protected”?

I have seen some very nice and enlightening awnsers to questions related to topological order and insulators, such as here, or here. However, I'm still puzzled by the concept of "symmetry protection" ...
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1answer
66 views

What is gate symmetry?

I just read this interesting interview with Frank Wilczek and he talks a couple of times about gate symmetry, without ever defining the term. This isn't a term I've come across, and google throws up ...
4
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1answer
59 views

Symmetries in physics (specifically condensed matter physics)

Symmetries play a big role in physics. Some symmetries are translation symmetry, rotation symmetry, time translation symmetry, timereversal symmetry etc. It seems that in condensed matter physics ...
3
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1answer
130 views

Why don't we observe spontaneous symmetry restoration in nature?

Why do we always observe spontaneous symmetry breaking in nature and not restoration? Does there exist some argument with the 2nd law of thermodynamics and the entropy of the universe increasing? If ...
8
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1answer
98 views

Why is a theory Lorentz invariant if the Lagrangian is Lorentz invariant?

For if I started by trying to make the Hamiltonian Lorentz invariant, I would have failed. Indeed, the Hamiltonian is part of a covariant tensor. But how do I know that the Lagrangian is not a part of ...
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1answer
54 views

Global Anomaly and Ward Identity

This question is a continuation of the answer posted for this question about anomalies. What happens to the Ward identity corresponding to a global symmetry if that symmetry is anomalous? I mean, is ...
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1answer
35 views

How does the surface of a material always break inversion symmetry?

I am trying to visualize this for an HCP structure. Take the profile view as such: just working in 2d. So my understanding is if we can take a point (x,y) -> (-x,-y) and get the same crystal than ...
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0answers
26 views

Spontaneous symmetry breaking of scalar multiplet theory

Consider a theory with two multiplets of real scalar fields $\phi_i$ and $\epsilon_i$, where $i$ runs from $1$ to $N$. The Lagrangian is given by: $$\mathcal L = \frac{1}{2} (\partial_{\mu} \phi_i) ...
3
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1answer
40 views

Generators of a certain symmetry in Quantum Mechanics

In Classical Mechanics to describe symmetries like translations and rotations we use diffeomorphisms on the configuration manifold. In Quantum Mechanics we use unitary operators in state space. We ...
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1answer
38 views

Properties of a body with spherical symmetry

I'm studing Gauss law for gravitational field flux for a mass that has spherical symmetry. Maybe it is an obvious question but what are exactly the propreties of a spherical simmetric body? A ...
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0answers
28 views

Transformation applied to system without symmetry

Imagine we have a central potential which gives us the Hamiltonian of the form: $$\hat H=-\frac{\hbar^2}{2m} \nabla^2 +V(r)$$ In general this is not symmetric under translation. But let us say that I ...
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1answer
45 views

Symmetry responsible for equality of masses of particles

During my studies of basic particle physics the following question came up. What symmetry is responsible for equality of masses of particles and their antiparticles? In particular, is this symmetry ...
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46 views

Example of a symmetry and the group with which it is modelled? [duplicate]

Could you please provide a specific example of a symmetry and the group with which it is modelled? I am beginner to study symmetry in physics, please answer with just an example. This question is ...
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0answers
19 views

Fermion Trucation

I recently posted about truncating fermions in supergravity Lagrangians and got a good answer about how this gives a vev to the bosonic content and therefore freezes it to a stationary point of the ...
4
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4answers
288 views

Noether's theorem for space translational symmetry

Imagine a ramp potential of the form $U(x) = a*x + b$ in 1D space. This corresponds to a constant force field over $x$. If I do a classical mechanics experiment with a particle, the particle behaves ...
0
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1answer
35 views

scalar potential and vector potential behave symmetry properties

How the scaler potential Q(x,t) and vector potential A(x,t) behave under parity and time-reversal transformations.
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64 views

What is physically irreducible representation?

When I use bilbao crystallographic server recently, I noticed a notation called physically irreducible representation. Paper says it is a direct sum of two complex conjugate representations (if ...
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23 views

Water dipole by symmetry argument [closed]

I'm a mathematician and I'm studying Group and Representation theory and I came across with an interesting exercise involving physics, although I don't know physics, since I'm a mathematician, I found ...
3
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1answer
37 views

Why does exchanging coordinates produce a phase of $\pm 1$ in an identical particle wavefunction?

Consider a system of two identical particles described by a wavefunction $\psi(x_1, x_2)$. There are two kinds of exchange operators one can define: Let $P$ be physical exchange. This operator swaps ...
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5answers
730 views

Why can a solution show optical rotation?

Why can a solution show optical rotation? A solution, as a liquid, is rotationally isotropic, right? So, even if the molecules are chiral, because of the random orientation of the molecules, shouldn't ...
4
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0answers
85 views

Completely positive maps and symmetric states

Let $\mathcal{N}$ be a completetely positive trace preserving map (aka a quantum channel) acting on a finite dimensional system $\mathrm{A}$, and let $\pi$ denote the maximally mixed state on ...
4
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2answers
40 views

Does a central force have to be independent of angle?

When defining a central force, some sources, like Wikipedia, say that the magnitude of the force only depends on the distance $r$: In classical mechanics, a central force on an object is a force ...
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0answers
14 views

Isolated system and mutual interaction potential

We know that the total linear momentum of a closed (isolated) system is conserved due to homogeneity of space (Landau and Liftshitz, page 15, Mechanics). Hence for an isolated system of two bodies ...
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2answers
113 views

Symmetry and degeneracy in quantum mechanics

If an operator commutes with the Hamiltonian of a problem, does it always must admit degeneracy? For example, parity operator commutes with the Hamiltonian in case of a free particle and we have two ...
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57 views

Why are symmetrical structures highly stable?

What makes symmetrical structures(geometry) highly stable? It is perfect to say that the forces acting on a symmetrical structure is balanced and hence stable. But why is it so? To be more specific, ...
4
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1answer
36 views

Symmetry Arguments: Flow Through Cylinder

Why can for symmetry reasons a steady, viscous, incompressible flow, obaying the N.S equation: $$\rho(v \nabla)v = -\nabla p + \eta \Delta v $$ That flows through a cylindrical(very long) pipe not ...
2
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0answers
26 views

$SU(2)$ symmetry and conservation law in condensed matter systems [closed]

My question has a few parts, I know from Noether that if there is a symmetry in a Hamiltonian, there is a conservation law. What would be the conservation law associated with $SU(2)$ symmetry? ...
7
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1answer
134 views

Invariant polynomials of the Landau theory of phase transitions (crystal symmetry?)

I'm convinced I'm missing something so obvious but here goes Typically, one can define something like a "general" expansion of an order parameter, ${\boldsymbol \Gamma}$, up to 6th order as follows ...
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1answer
42 views

Is it necessary to prove the existence of an operator representing symmetry on Hilbert space?

Is there any need to prove the existence of an operator $U$ which represents the action of symmetry transformation on rays in Hilbert space? Or is it enough just to prove that it is unitary and linear ...
0
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1answer
88 views

Deeper principles in classical mechanics

While teaching introductory physics, my professor explained that the conservation of linear momentum, conservation of energy and conservation of angular momentum are based on deeper principles in ...
0
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1answer
49 views

Coleman Mandula theorem and translations

I don't know what Coleman Mandula theorem is, however if I were forced to say something about it, I will say it is a statement that suggests that internal and spatial symmetries have no unique ...
4
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0answers
64 views

Derivations of Newton's laws?

I feel convinced that the mathematics behind newtons laws can be derived from Noether's symmetry theorems. The fact that displacement s can be described by a cartesian coordinate system with a ...