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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Precise statement of Mermin–Wagner theorem

Roughly speaking, Mermin-Wagner theorem states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions ...
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Categorizing solutions to Hierarchy problem

We know that no gauge symmetry can prevent a term $m_\phi^2|\phi|^2$ for a scalar field, and that, given the quadratic loop corrections, the natural scale is $m_\phi \sim M_P$. This is related to the ...
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178 views

Some questions about the edge states for time-reversal invariant topological superconductors?

Stimulated by my some recent calculations on edge states(ES) for time-reversal invariant(TRI) topological superconductors(TS) as well as many questions concerning the "edge states" in Physics ...
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49 views

Diagonal matrix in k-space

I'm having some trouble with an integration I hope you guys can help me with. I have that: ${{\mathbf{v}}_{i}}\left( \mathbf{k} \right)=\frac{\hbar {{\mathbf{k}}_{i}}}{m}$ and ...
2
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1answer
96 views

Topological vs. non-topological noetherian charges

What (if any) is the relationship between the conserved (non-topological) noetherian charges and topological charges? Namely, is there any "generalization" of the Noether's first theorem that includes ...
5
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94 views

Gauging discrete symmetries

I read somewhere what performing an orbifolding (i.e. imposing a discrete symmetry on what would otherwise be a compactification torus) is equivalent to "gauging the discrete symmetry". Can anybody ...
2
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1answer
155 views

Possible states for two electrons in the helium atom

Consider the helium atom with two electrons, but ignore coupling of angular momenta, relativistic effects, etc. The spin state of the system is a combination of the triplet states and the singlet ...
2
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1answer
272 views

Baryon wave function symmetry

If a baryon wavefunction is $\Psi = \psi_{spatial} \psi_{colour} \psi_{flavour} \psi_{spin}$, and we consider the ground state (L=0) only. We know that the whole thing has to be antisymmetric under ...
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99 views

A general wavefunction in a square lattice

Suppose we have a square lattice with periodic condition in both $x$ and $y$ direction with four atoms per unit cell, the configuration of the four atoms has $C_4$ symmetry. What will be a general ...
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43 views

Coordinate transform to exploit symmetry

I have a stochastic process that can be described the following master-equation: $$ \partial_{t}P(x,y)=-\left(W_{12}(x,y)+W_{13}(x,y)+W_{21}(x,y)+W_{23}(x,y)+W_{31}(x,y)+W_{32}(x,y)\right)P(x,y)\\ ...
4
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1answer
110 views

“WLOG” re Schwarzschild geodesics

Why, when studying geodesics in the Schwarzschild metric, one can WLOG set $$\theta=\frac{\pi}{2}$$ to be equatorial? I assume it is so because when digging around the internet, most references seem ...
3
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1answer
384 views

How to define the mirror symmetry operator for Kane-Mele model?

Let us take the famous Kane-Mele(KM) model as our starting point. Due to the time-reversal(TR), 2-fold rotational(or 2D space inversion), 3-fold rotational and mirror symmetries of the honeycomb ...
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84 views

Curie's principle in electromagnetic field theory

I am looking for some explanation and if possible also some references about the applications of Curie's principle in electromagnetic field Theory, precisely in the computation of magnetic (resp. ...
4
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2answers
496 views

Spherical charge in two different dielectric materials

I am trying to freshen up my memory about electrical fields and I came across this exercise from school. A sphere with a constantly distributed charge is located in between two different dielectrics ...
6
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0answers
251 views

Extended Born relativity, Nambu 3-form and ternary (n-ary) symmetry

Background: Classical Mechanics is based on the Poincare-Cartan two-form $$\omega_2=dx\wedge dp$$ where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. By the other hand, ...
2
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1answer
296 views

Invariance, covariance and symmetry

Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? ...
18
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4answers
578 views

When can a global symmetry be gauged?

Take a classical field theory described by a local Lagrangian depending on a set of fields and their derivatives. Suppose that the action possesses some global symmetry. What conditions have to be ...
8
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3answers
497 views

What is kappa symmetry?

On page 180 David McMohan explains that to obtain a (spacetime) supersymmetric action for a GS superstring one has to add to the bosonic part $$ S_B = -\frac{1}{2\pi}\int d^2 \sigma ...
3
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2answers
139 views

What is a symmetry of a physical system?

If I understand correctly, in many context in physics (quantum mechanics?), a physical system is specified by giving its Hamiltonian. I also hear that symmetries are rather essential. As far as the ...
3
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1answer
134 views

Gravitational field v.s. Physical variable?

I went to a talk on Newtonian mechanics some time earlier and the speaker said, and I quote, Newton's equations of motion admit a larger symmetry group than the Galilean group alone. Therefore, ...
6
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2answers
801 views

A question on the existence of Dirac points in graphene?

As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2$\times$2 Hermitian matrix $H(k_x,k_y)$ has two degenerate points $K$ ...
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69 views

CP-symmetry and Ward identities and finite temperature

I have a few questions about Ward-identities which I summarize here. For each I am very greateful for answers and references to literature. Wikipedia states about Ward-identities: The ...
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1answer
89 views

A simple example of symmetry setting the properties of a Physical System

Does anybody know of an example were one could derive some important properties of a physical system from a symmetry of said system. I´m specially looking for simple classical examples, which could ...
3
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1answer
210 views

What are the conserved charges related to the Virasoro generators?

I have just learned from reconsidering my demystified book, that when conformally maping the worldsheet of a closed string to the complex plain by using the transformation $z = e^{\tau + i\sigma}$ ...
4
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1answer
553 views

A simple model that exhibits emergent symmetry?

In a previous question Emergent symmetries I asked, Prof.Luboš Motl said that emergent symmetries are never exact. But I wonder whether the following example is an counterexample that has exact ...
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140 views

Question about Noether theorem

For the Noether theorem for pseudoeuclidean 4-spacetime a-current $J_{a}^{\mu}$ is equal to $$ J_{a}^{\mu} = \frac{\partial L}{\partial (\partial_{\mu}\Psi_{k})}Y_{k, a} - \left( \frac{\partial ...
2
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1answer
112 views

Lorentz invariance of the wave equation

I want to show that the 2-d wave equation is invariant under a boost, so, the starting point is the wave equation $$\frac{\partial^2\phi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2\phi}{\partial ...
2
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1answer
107 views

Energy-momentum conservation without translation symmetry?

As I checked, the energy-momentum tensor defined as ${T^\mu}_\nu=\frac{\partial {\cal L}}{\partial(\partial_\mu \phi)}\partial_\nu \phi-{\cal L}{\delta^\mu}_\nu$ at the solution $\phi$ of equation of ...
2
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3answers
751 views

Noether's current expression in Peskin and Schroeder

In the second chapter of Peskin and Schroeder, An Introduction to Quantum Field Theory, it is said that the action is invariant if the Lagrangian density changes by a four-divergence. But if we ...
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2answers
171 views

Eigenfunctions in periodic potential

For Hamiltonian $\operatorname H$ and lattice translation operator $\operatorname T$, if $$\operatorname H\psi=E\psi, \qquad \operatorname T\psi=e^{ik\cdot R}\psi,$$ and $$\operatorname ...
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2answers
1k views

Galilean invariance of the Schrodinger equation

I am only asking this question so that I can write an answer myself with the content found here: http://en.wikipedia.org/wiki/User:Likebox/Schrodinger#Galilean_invariance and here: ...
19
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1answer
1k views

Emergent symmetries

As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
9
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5answers
465 views

Form of the Classical EM Lagrangian

So I know that for an electromagnetic field in a vacuum the Lagrangian is $\mathcal L=-\frac 1 4 F^{\mu\nu} F_{\mu\nu}$, the standard model tells me this. What I want to know is if there is an ...
5
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2answers
174 views

Crystal Angular Momentum

In a crystal, we don't have full translational symmetry, but we still have discrete translations. This allows us to define "crystal momentum" that is conserved modulo a reciprocal lattice vector. In ...
3
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2answers
95 views

What symmetries does a lattice calculation need to preserve?

I've heard that it is impossible to have a properly Lorentz-invariant lattice QFT simulation, as the Lorentz invariance is spoiled by the nonzero lattice distance $a$. I've also heard that there are ...
14
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1answer
406 views

Spontaneous breaking of Lorentz invariance in gauge theories

I was browsing through the hep-th arXiv and came across this article: Spontaneous Lorentz Violation in Gauge Theories. A. P. Balachandran, S. Vaidya. arXiv:1302.3406 [hep-th]. (Submitted on 14 ...
4
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1answer
122 views

Dimensional transmutation in Gross-Neveu vs others

Firstly I don't know how generic is dimensional transmutation and if it has any general model independent definition. Is dimensional transmutation in Gross-Neveau somehow fundamentally different ...
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40 views

Residual symmetries of the superposition of two fcc lattices

Fcc lattices are Bravais lattices and so are invariant under a set of discrete translations plus inversions over the 3 axis ($x\rightarrow -x$,$y\rightarrow -y$,$z\rightarrow -z$). When one superposes ...
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2answers
740 views

Why and how does symmetry work in circuits?

Why symmetry work in circuits? In my book there is no mention explanation as such for symmetry arguments and circuits. But there are circuits that are very difficult to solve without symmetry. Also I ...
4
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1answer
223 views

How do we make symmetry assumptions rigorous?

I have, for instance, a problem with a spherically symmetric charge distribution. I deduce here, in order to solve the problem easily, that the corresponding electric field must be symmetric. How is ...
3
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2answers
238 views

Any example of lower symmetry in high temperature phase than the low temperature phase?

All the phase transition cases I came across so far have this property: the lower temperature phase has lower symmetry than the higher temperature one. But it is nowhere explicitly said that, lower ...
6
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1answer
154 views

Are group representations possible when the solution space is not a vector space?

As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector ...
2
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2answers
197 views

Does a constant factor matter in the definition of the Noether current?

This is a very basic Lagrangian Field Theory question, it is about a definition convention. It takes much more time to typeset it than answering, but here it is: Consider a field Lagrangian with only ...
15
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2answers
374 views

Coulomb gauge fixing and “normalizability”

The Setup Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as $$ A_\mu\to ...
5
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1answer
1k views

Physical significance of Killing vector field along geodesic

Let us denote by $X^i=(1,\vec 0)$ the Killing vector field and by $u^i(s)$ a tangent vector field of a geodesic, where $s$ is some affine parameter. What physical significance do the scalar quantity ...
2
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0answers
45 views

How does a snowflake “know” to form symmetrically? [duplicate]

Possible Duplicate: Why are snowflakes symmetrical? Under ideal situations, a snowflake forms into near perfect hexagonal symmetry. How? For instance, when a water molecule moves towards ...
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2answers
92 views

Why does isotropy principle require existence of inertial transformation when axes are reversed?

Assuming one spatial and one termporal dimension, let's assume an intertial transformation $A(v)$ as follows: $$ \begin{pmatrix} t' \\ x' \\ \end{pmatrix} = A(v) \begin{pmatrix} t \\ x \\ ...
8
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1answer
530 views

Do an action and its Euler-Lagrange equations have the same symmetries?

Assume a certain action $S$ with certain symmetries, from which according to the Lagrangian formalism, the equations of motion (EOM) of the system are the corresponding Euler-Lagrange equations. Can ...
18
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899 views

Elegant approaches to quantum field theory

I have been reading Quantum Mechanics: A Modern Development by L. Ballentine. I like the way everything is deduced starting from symmetry principles. I was wondering if anyone familiar with the book ...
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1answer
160 views

Killing Vectors of BTZ black hole and their calculation in general

I was wondering what are the Killing vectors of BTZ black hole and how to guess them easily? Will it be the same as of AdS? What then will be Killing vectors for AdS-Schwarzschild e.g.?