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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Is the converse of Noether's first theorem true: Every conservation law has a symmetry?

Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is the converse true: Any conservation law of a physical ...
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63 views

Given potentials, how does one find conserved quantities using Noether's theorem?

I've been asked to find the conserved quantities of the following 3D potentials: $U(\vec{r}) = U(x^2)$, $U(\vec{r}) = U(x^2 + y^2)$ and $U(\vec{r}) = U(x^2 + y^2 + z^2)$. For the first one, ...
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31 views

Does the similarity of gamma matrices correspond to a conserved quantity?

Gamma matrices have a similarity property, $\gamma^\mu\to S\gamma^\mu S^{-1}$ is a good transformation. Does this transformation correspond to a symmetry of the QED Lagrangian?
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32 views

normal degeneracy and the “span” of an irreducible representation

In Tinkham's "Group Theory and Quantum Mechanics", Tinkham defines normal degeneracy so that the span of the action of the Hamiltonian's symmetry group on any energy eigenstate yields all possible ...
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1answer
102 views

Quasicrystals - Projections from higher dimensional regular crystal lattices

Why are quasicrystals projections from higher dimensional regular crystal lattices? See for example wikipedia: »Mathematically, quasicrystals have been shown to be derivable from a general ...
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1answer
71 views

Why Levi-Civita term signal the breaking of parity and time reversal?

For example, referring to Zee's QFT book, in Chern-Simons matter theory, after writing a term $$\gamma {\varepsilon ^{\mu \nu \lambda }}{a_\mu }{\partial _\nu}{a_\lambda }$$ he said The ...
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1answer
111 views

Does a symmetry necessarily leave the action invariant?

A symmetry maps a configuration with stationary action to another configuration with stationary action. However, does it necessarily preserve the value of the action exactly? It seems that it should ...
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1answer
82 views

Does an on-shell symmetry necessarily change the Lagrangian by a total derivative?

This is a follow-up question to: Does a symmetry necessarily leave the action invariant? Qmechanic writes here: Here the word off-shell means that the Lagrangian eqs. of motion are not assumed to ...
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1answer
34 views

How to show OPE coefficients are symmetric in three indices ?

May it is very trivial, but I am stuck here, given (I have suppressed the conjugate coordinates) $$ \phi_i(x) \phi_j(y) \sim \sum_{k} c_{ijk} (x-y)^{h_k - h_i - h_j} \phi_k(y) $$ $$ \langle ...
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137 views

Derivation of Rashba spin-orbit coupling in tight-binding model

Rashba spin-orbit coupling Hamiltonian in free space can be written as: $H_{\text{so}}=\int d^3r \Psi^{\dagger}(\mathbf{r}) \gamma (p_{x}\sigma _{y}-p_{y}\sigma _{x})\Psi(\mathbf{r})$. I expand ...
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1answer
84 views

Problem with determining number of goldstone bosons

Consider a theory $$\mathcal{L}=(\partial_\mu\Phi^\dagger)(\partial^\mu\Phi)-\mu^2(\Phi^\dagger\Phi)-\lambda(\Phi^\dagger\Phi)^2$$ where $\Phi=\begin{pmatrix}\phi_1+i\phi_2\\ ...
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1answer
53 views

Infinitesimal transformations and Poisson brackets [duplicate]

I want to understand how bracket operations in general are related to symmetry and infinitesimal transformations (in hindsight of quantumfieldtheory), so I calculated an example with a particle that ...
3
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1answer
51 views

How to quantify translational symmetry?

I'm trying to study phase transitions and I'm trying to find a way to classify regions of space based on their "crystallinity". I'm working with 3D coordinates, but I'll present the problem in 2D ...
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1answer
221 views

Noether's Theorem: Lie algebra, Lie groups

I've had a brief look through similar threads on this topic to see if my question has already been answered, but I didn't find quite what I was looking for, perhaps it is because I'm finding it hard ...
7
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1answer
292 views

Noether currents in QFT

I am trying to organize my knowledge of Noether's theorem in QFT. There are several questions I would like to have an answer to. In classical field theory, Noether's theorem states that for each ...
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0answers
55 views

Conserved charge of a conformal transformation

From Becker, Becker and Schwarz String Theory and M-Theory: For the infinitesimal conformal transformation $$\tag{3.25}\delta z=\varepsilon(z)\quad\text{and}\quad \delta\bar ...
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111 views

How can gauge invariance be unphysical?

Gauge symmetry is said to be "unphysical" because the transformations - unlike changes of reference frame - do not correspond to real physical operations. But the consequences of gauge symmetries are ...
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1answer
34 views

Silicon: conduction band minima

Why do the energetic minima of the silicon conduction band lie not in a high-symmetry point like a $X$-point, but somewhere in $\Delta$-direction between points $\Gamma$ and $X$? What is the physical ...
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1answer
99 views

Schrodinger equation, commutative operators, and Symmetry

When solving Schrodinger's equation in 3D with a spherical laplacian you reach a point at which you introduce a separation constant and can see that the same eigenvalue satisfies the radial and ...
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3answers
117 views

Ideal, isotropic fluid and stress tensor

An ideal fluid is the one which cannot support any shearing stress. It also doesn't have viscosity. My question is what does it mean by a fluid to be isotropic? Is an ideal fluid necessarily isotropic ...
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3answers
209 views

How to understand this symmetry in the wavefunctions of a diatomic molecule?

In Wikipedia (and elsewhere), a particular symmetry of the quantum system of a diatomic molecule is mentioned: symmetry under reflection along a plane containing the internuclear axis. The ...
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0answers
107 views

What is the symmetry group of this Hamiltonian?

Consider a Hamiltonian $$\hat H=-\partial_x^2-\partial_y^2+(x-y)Q,$$ where $x,y\in[0,a]$ (homogeneous Dirichlet boundary conditions assumed), and $Q$ is some real parameter. When $Q=0$, the ...
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1answer
71 views

Relation between gauge symmetry and mass difference

Usually (like in Georgi's Lie Algebra book) people argue the reason why Gellmann $SU(3)$ flavor symmetry (u,d,s) can't extend to $SU(4)$ (u,d,c,s) or higher flavour symmetry is the their mass ...
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0answers
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What is the difference between the groups $PSU(N)$ and $SU(N)$? [closed]

What is the difference between the groups $PSU(N)$ and $SU(N)$? For example how is $PSU(2,2|4)$ different than $SU(2,2|4)$?
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7answers
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What does the statement “the laws of physics are invariant” mean?

In the first paragraph of Wikipedia's article on special relativity, it states one of the assumptions of special relativity is the laws of physics are invariant (i.e., identical) in all inertial ...
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Does point group symmetry also act within “spin space” for a lattice spin system?

As an example, let's consider a quantum spin system on a 2D square lattice. The lattice point group symmetries include $C_4$ rotation, parities, etc.... And let's take $C_2$ symmetry (2-fold rotation) ...
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$SO(3)$, $SU(2)$ and symmetries in quantum mechanics [duplicate]

A rotation in the vector space $\mathbb{R}^3$ is represented by the known 3x3-matrices. But at this point I'm really confused how to get from there to Quantum Mechanics. The group of ...
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1answer
64 views

Why does Weyl invariance imply a traceless energy-momentum tensor?

I've begun to self-study String Theory from Polchinski and Becker, Becker and Schwarz. I don't see why the fact that the Polyakov action is invariant under Weyl transformations is related to the ...
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2answers
208 views

Changing vector basis in AdS$_3$

I have AdS${}_3$ given as a surface embedded in a 4 dimensional pseudo-Riemannian space $$x^2+y^2-u^2-y^2=-l^2$$ With metric: $$ds^2=dx^2+dy^2-du^2-dv^2$$ I have Killing vectors of that space ...
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153 views

What are spin and valley symmetries in graphene?

I have been assigned a presentation on a part of a paper (http://arxiv.org/abs/1303.6942). My task is to present on the spin and valley symmetries in graphene, and relate it back to the paper above. ...
4
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2answers
83 views

Definition of Duality (opposed to Symmetry)

I'm learning basic string theory right now and we came across T-duality which was presented as a symmetry of the formula for the mass of a string in the context of compactification. There was a remark ...
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30 views

Can any global symmetry be promoted to the local symmetry? [duplicate]

Can any global symmetry be promoted to the local symmetry? Does there exist counterexample?
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1answer
198 views

What exactly do we mean by symmetry in physics?

I'm referring here to invariance of the Lagrangian under Lorentz transformations. There are two possibilities: Physics does not depend on the way we describe it (passive symmetry). We can choose ...
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2answers
136 views

Global symmetry and particle multiplets

In chapter 20, of Peskin and Schroeder's quantum field theory book, they start with a comment that a global symmetry that is manifest lead to particle multiplets with restricted interactions. Can ...
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209 views

Is there a mathematical reason for the Lagrangian to be Lorentz invariant?

The Hamiltonian is the energy, which is just one component of a four-vector and therefore not Lorentz invariant. The Lagrangian is the Legendre transform of the Hamiltonian and I was wondering if ...
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2answers
113 views

How can I prove that $\langle\Omega\vert \phi(x) \vert\Omega\rangle \langle\Omega\vert\phi(y)\vert\Omega\rangle=0$ for a scalar field?

From Peskin-Schroeder, p.212: The term $$ \langle \Omega | \phi(x) | \Omega \rangle \langle \Omega |\phi(y) | \Omega \rangle$$ is usually zero by symmetry; for higher-spin fields, it is zero ...
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1answer
203 views

Does time invariance conclude conservation of energy? [closed]

I find it hard to understand that time-translation invariance necessarily implies conservation of energy. As I understand it, Noether's theorem says that there is an energy conservation because the ...
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1k views

Symmetrizing the Canonical Energy-Momentum Tensor

The Canonical energy momentum tensor is given by $$T_{\mu\nu} = \frac{\partial {\cal L}}{\partial (\partial^\mu \phi_s)} \partial_\nu \phi_s - g_{\mu\nu} {\cal L} $$ A priori, there is no reason to ...
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1answer
47 views

What conserved quantities does a one-dimensional non-symmetric lattice have?

When I asked what leads to degeneracy of eigenstates of free particle, the answer was parity. But it appears that even if we consider a lattice with non-symmetric cell, so the potential looks as shown ...
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213 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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1answer
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How to diagonalise the Lagrangian mass term with SU(4) symmetry and self-dual tensors

I should write the mass term of the Lagrangian with global SO(4) symmetry in tensor representation with anti-symmetric tensors and then diagonalise this term with defining a new set of tensors ...
2
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0answers
56 views

Weaker Formulations of Bulk-boundary Correspondence for Interacting Systems

From this post, it seems that bulk-boundary correspondence does not hold in general for interacting systems. What is meant by bulk-boundary correspondence there appears to be the existence of robust ...
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1answer
36 views

Finding a basis for minimal representation of a wavefunction (extracting symmetries)

I asked something like this on Math StackExchange, but now that I think about it, this probably belongs better over here. I want to find all linear operators (non necessarily hermitian) $\{\hat{A}\}$ ...
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3answers
161 views

Do algorithms have an intrinsic time direction?

This article says There is no intrinsic time direction in Newton's mechanics nor in the differential equations of the new physics. My question is, do other types of mathematics, say a cellular ...
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0answers
120 views

Does Noether's theorem apply to entropy?

Entropy appears to have a translation symmetry - adding some constant value to it doesn't appear to my fairly rudimentary understanding of physics alter the actual physics. Is this correct? Now ...
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1answer
202 views

Why do we need spontaneous symmetry breaking in Lagrangian formalism?

I have always struggled with the concept of spontaneous symmetry breaking. It seems to me that many others don't find it very intuitive as well, but that could be just me having difficulties with the ...
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1answer
168 views

Why are large scale structures isotropic in the Ising model?

I have at least a qualitative understanding of why the critical state of the Ising model is scale invariant, by arguments to do with renormalisation, which I understand only very roughly. However, in ...
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1answer
338 views

Solving Special Function Equations Using Lie Symmetries

The lie group + representation theory approach to special functions & how they solve the ode's arising in physics is absolutely amazing. I've given an example of it's power below on Bessel's ...
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Explain materials with 4 fold symmetry having same reflectance when shone with LCP and RCP

This is my first post here. I am currently reading "Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation" by Do-Hoon Kwon, Pingjuan L. Werner, and ...
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75 views

Question about global internal $SO(n)$ symmetry

I have the following Lagrangian (density) for bosons $$L = \partial_{\mu} \phi^i \partial^{\mu}\phi^i+ m^2\phi^i \phi^i$$ and I am trying to understand why this Lagrangian is invariant under ...