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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Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
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238 views

Symmetries of the Standard Model: exact, anomalous, spontaneously broken

There are a number of possible symmetries in fundamental physics, such as: Lorentz invariance (or actually, Poincaré invariance, which can itself be broken down into translation invariance and ...
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542 views

Gauge redundancies and global symmetries

It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ...
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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, ...
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53 views

What is the definition of integrability in the context of surface charges?

In the usual covariant approach to the development of surface charges of an asymptotic symmetry group, one works with the linearized theory as this ensures that the charges are integrable. I also ...
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114 views

Questions on Penrose's paper - Conformal Treatment of Infinity

I have several questions. Perhaps it would be better to separate them into different posts. However, given their relative closeness to each other, I think putting it all in one place would be better. ...
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322 views

Symmetrizing the Canonical Energy-Momentum Tensor

The Canonical energy momentum tensor is given by $$T_{\mu\nu} = \frac{\delta {\cal L}}{\delta (\partial^\mu \phi_s)} \partial_\nu \phi_s - g_{\mu\nu} {\cal L} $$ A priori, there is no reason to ...
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28 views

What groups of symmetry are most suited for filling uniformely a spherical 3D space, whilst possessing the lowest possible surface-to-volume ratio?

I am looking for the closest known approximate solution to Kelvin foams problem that would obey a spherical symmetry. One alternative way of formulating it: I am looking for an equivalent of ...
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116 views

Time Reversal in Euclidean Spacetime - unitary or antiunitary?

(pre-request) We know that time reversal operator $T$ is an anti-unitary operator in Minkowsi Spacetime. i.e. $$ T z=z^*T $$ where the complex number $z$ becomes its complex conjugate. See, for ...
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88 views

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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53 views

Complex scalar fields conserved charges

I'm currently studying field theory and I'm having some trouble with conserved charge given in field components. If we have a complex scalar action of a field $\phi=(\phi_1,\phi_2)^T$ that is ...
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124 views

Does the projected spin state of the $d+id$ mean-field Hamiltonian on a triangular lattice has time-reversal(TR) symmetry?

Consider the following $d+id$ mean-field Hamiltonian for a spin-1/2 model on a triangular lattice $$H=\sum_{<ij>}(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$$, with $\chi_{ij}=\begin{pmatrix} 0 & ...
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91 views

Some hints for special case of metric tensor in GR

Let's have metric $$ ds^2 = dt^2 - dx^2 - dy^2 - dz^2 - 2f(t - z, x, y)(dt - dz)^2. $$ I need to prove that it is an exact solution for Einstein equations in vacuum for $\partial_{x}^{2}f + ...
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254 views

Killing vectors for 2-sphere as generators of $SO(3)$ symmetry

How to get Killing vectors in a form of generators of $SO(3)$ group symmetry? By using Killing equations for metric $ds^{2} = d\theta^{2} + \sin^{2}(\theta^{2}) d\varphi^{2}$ I got $$ ...
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68 views

What does the term 'a uniform RVB spin-liquid state' mean?

I encountered this term a uniform RVB spin-liquid state in some articles, for example, see the paragraph under Eq.(29) on page 9 in this paper. What does the word 'uniform ' mean? Simply from the ...
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159 views

Some ambiguous points on Spontaneous Symmetry Breaking (SSB)?

Almost in every textbook of condensed matter physics, the standard description of SSB could be formulated as follows: Consider the lattice Heisenberg model in an external magnetic field ...
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198 views

Traceless of stress-energy tensor in $d=2$

This is a question regarding Francesco, section 4.3.3. In this section, he considers the two-point function $$ S_{\mu\nu\rho\sigma}(x) = \left< T_{\mu\nu}(x) T_{\rho\sigma}(0)\right> $$ He then ...
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185 views

Method of images tutorial?

I'm having an exam in Electrodynamics soon. I think I have most of it under control, but the method of images I'm not quite sure about. There is not much in my book about, so I was thinking some of ...
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166 views

Who used the concept of symmetries first?

Who "invented" the concept of symmetries? This article is quite extensive, but it blurs the history with the modern understanding. http://plato.stanford.edu/entries/symmetry-breaking/ Some of the ...
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174 views

Symmetries of separable potential

For separable potential, say $x^4+y^4$, its symmetry are degenerate. Is that a generic case to every separable potential? I will explain my question: The potential $x^4+y^4$ has $A_1, B_1, A_2, B_2, ...
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77 views

Solving the Schrodinger equation with appropriate symmetry

In the paper Markov Fields by Edward Nelson the introduction section claims that analytically continuing a Markov process with appropriate symmetry properties yields the solution of the Schrodinger ...
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76 views

How symmetry is related to the degeneracy?

I have several questions about symmetry in quantum mechanics. It is often said that the degeneracy is the dimension of irreducible representation. I can understand that if the Hamiltonian has a ...
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25 views

Casimir Invariants of the Galilean group

I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I ...
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88 views

Parity violating Dirac particle

We normally write down the Dirac Lagrangian as \begin{equation} {\cal L} _D = \bar{\psi} ( i \partial _\mu \gamma ^\mu - m ) \psi \end{equation} but are the Lagrangian's, \begin{equation} ...
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98 views

Maxwell equations and symmetry

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry? I believe the homogeneous Maxwell equations obey parity and time ...
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259 views

What is the definition of particle-hole symmetry in condensed matter physics?

People often talk about particle-hole symmetry in solid state physics. What are the exact definition and physics picture of particle-hole symmetry? How to define the density of particles and holes?
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63 views

Can classical orders coexist with quantum orders?

For example, the ground state of the antiferromagnetic(AFM) Heisenberg model $H=J\sum_{<ij>}\mathbf{S}_i \cdot \mathbf{S}_j(J>0)$ on a 2D square lattice is a Neel state, which is a classical ...
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149 views

Tree level and loop level

I'm trying to read through a paper which explains the following about Universal Extra Dimensions (UED) vs ADD models: The new feature of the UED scenario compared to the brane world is that ...
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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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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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295 views

Influence of Joe Rosen work, is it marginal, or significantly accepted?

I have prepared a paper that relies on work of Joe Rosen on symmetry (e.g. "Symmetry Rules: How Science and Nature Are Founded on Symmetry"). I am wondering about his influence. For example, when I ...
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57 views

Reissner-Nordström Black Holes

The Reissner-Nordström black holes are described by the metric, \begin{align} ds^2 = -\left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\right)dt^2 + \frac{1}{1-\frac{2M}{r}+\frac{Q^2}{r^2}}+r^2d\Omega^2 ...
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72 views

Linearized gravity and symmetries

I have naive question. When we analyzing weak gravity field we introduce expression for metric tensor as $$ g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}, \quad \eta_{\mu \nu} = diag(1, -1, -1, -1), ...
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104 views

Scale-invariant differential operator

For example, the differential operator Laplacian is $$\nabla^2 = \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}.$$ My questions are: Is it scale-invariant? what is ...
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121 views

Renormalization, symmetries and freedom to choose counterterms

I am considering the perturbative renormalization of a simple non-phenomenological QFT with Lagrangian ${\cal L}$ (for scalar fields with multiple generations). I understand that I can renormalize it, ...
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87 views

Spontaneous symmetry breaking by axions?

I am just reading at the beginnin of this nice article, that axions could be responsible for spontaneously breaking of a symmetry in the early universe. Does anybody know which symmetry is alluded to ...
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56 views

Global part of a local symmetry?

What is exactly meant by "Global part of a Local symmetry"? What are its implications on a field theory at classical level? What are its implications at quantum level? How is it related to symmetry ...
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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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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 ...
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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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147 views

Why does renormalization need an unbroken symmetry?

Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ...
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192 views

Breaking of conformal symmetry

I am wondering something about the breaking of conformal symmetry: I know that it can be broken at the quantum level, anomalously, but I never encountered or heard about a model where it is broken "à ...
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Forces, symmetry, and asymmetry

The concept of symmetry is one of the most promising and misunderstood concepts in physics. If one consider Hermann Weyl ("Symmetry"; ISBN-13: 978-0691023748), "As far as I see, all a priori ...
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81 views

what kind of system respects $SU(N)$ symmetry?

I read this post, Is the symmetry group of two spin 1/2 particles $SU(2) \times SU(2)$ or $SU(4)$? If the picked answer is correct, can I believe that an $N$-degenerate system respects $SU(N)$ ...
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35 views

Symmetry argument about degeneracy of graphene energy band at Dirac point

This question is very related to the thread here. In the answer given by @BebopButUnsteady , the statement is that as long as the inversion and time-reversal symmetry are respected, the Dirac points ...
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43 views

Lepton number conservation and global phase transformation

Why the lepton number conservation is connected with the invariance of the lagrangian under global phase (U(1)) transformation of the wave function? How to distinguish global gauge phase and global ...
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60 views

Symmetry of wave pulse

How can one decide whether a wave pulse is symmetrical by looking at its equation? $$y(x,t)=\frac{0.8}{[4x+5t]^2} $$ represents a moving pulse will it be symmetric?
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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)\\ ...
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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. ...
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99 views

Dilatations in non-relativistic QM and operator tranformation

I was looking at a QM textbook exercise dealing with dilatations, the transformations are $x \rightarrow x' = \lambda x$ transforming $|\psi\rangle$ into $|\psi'\rangle = ...