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.

learn more… | top users | synonyms

2
votes
0answers
42 views

Antimatter universe and Noether's theorem

I am studying Feynman's "symmetry in physical laws", where he talks about conservation laws for corresponding symmetries. (I know this is Noether's theorem, I am studying this from David Tong's ...
2
votes
1answer
75 views

Symmetries of the action of the free classical Klein-Gordon field

I've read that the action for the free classical Klein-Gordon field $$S = \int \mathrm{d}^4x~ \mathcal{L} = \frac{1}{2} \int \mathrm{d}x^4 \left(\partial_\mu \phi(x) \, \partial^\mu \phi(x) - ...
1
vote
2answers
78 views

What are the unitary operators for various transformation?

Transformations, at least in lagrangian-symmetries context, are usualy described as uintary operators. I dont understand what are these operators exactly. For example, let's look at the Lorentz ...
2
votes
1answer
202 views

Symmetries of a Uniform Magnetic Field

Simple question. A system with a uniform electric field everywhere in space has translational invariance in the directions perpendicular to the electric field but no translational invariance parallel ...
0
votes
0answers
28 views

Landau theory of phase transation

In his article http://www.ujp.bitp.kiev.ua/files/journals/53/si/53SI08p.pdf, Landau defines probability distribution $\rho$ which is related to symmetry of crystal. If crystal has certain symmetry ...
3
votes
1answer
167 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 & ...
4
votes
3answers
189 views

Is Parity really violated? (Even though neutrinos are massive)

The weak force couples only to left-chiral fields, which is expressed mathematically by a chiral projection operator $P_L = \frac{1-\gamma_5}{2}$ in the corresponding coupling terms in the Lagrangian. ...
4
votes
2answers
125 views

Spontaneous Symmetry Breaking - struggling with physics based understanding?

Although I am a mathematician by nature, I'm writing an essay in my third year of my undergraduate on Spontaneous Symmetry Breaking in Physics, and as such I've become a little confused by how the ...
9
votes
4answers
273 views

Seeking a quality plain-language description of the Wigner-Eckart theorem

I'm a third year physics undergrad with a very cursory knowledge of quantum mechanics and the formalism involved. For instance, I understand roughly how tensors work and what it means for a tensor to ...
2
votes
2answers
288 views

Two puzzles on the Projective Symmetry Group(PSG)?

Recently I'm studying PSG and I felt very puzzled about two statements appeared in Wen's paper. To present the questions clearly, imagine that we use the Shwinger-fermion ...
8
votes
3answers
209 views

What is the symmetry associated with the local particle number conservation law for fluid?

According to Noether's theorem, every continuous symmetry (of the action) yields a conservation law. In fluid, there is a local particle number conservation law, which is ...
0
votes
1answer
83 views

Symmetry argument for a toroid?

When using Ampere's law for a toroid (in the toroid and around a circular path) please can someone explain the symmetry argument (or an alternative argument) which allows us to assume the field is ...
0
votes
2answers
34 views

How to define conserved charges in Euclidean field theory?

In a field theory with signature (1,d), conserved charges are obtained by integrating the time component of a conserved current over a spatial region. What are the corresponding equations and ...
2
votes
1answer
38 views

Parity transformation is proper orthochronous?

In 3+1 dimensional spacetime the parity transformation is $$P^\mu_{\;\,\nu}=\begin{pmatrix}+1&&&\\&-1&&\\&&-1&\\&&&-1\end{pmatrix}.$$ This is ...
2
votes
1answer
25 views

Parameterization of an arbitrary element of $U(2)_L \times U(2)_R$ (Chiral symmetry with two quarks)

When you write down the Lagrangian for two quarks : \begin{equation} \mathcal{L}_\text{QCD}^0 = -\frac{1}{4} G_{\mu\nu}^a G^{a\mu\nu}+ \bar\Psi i \gamma^\mu D_\mu \Psi \end{equation} you find an ...
5
votes
3answers
503 views

The Asymmetry between Real and Imaginary in the three Pauli Spin Matrices

The Pauli spin matrices $$ \sigma_1 ~=~ (\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix}), \qquad\qquad \sigma_2 ~=~ (\begin{smallmatrix} 0 & -i \\ i & 0 ...
0
votes
1answer
53 views

How do states in Hilbert Space act like irreducible representations?

I am reading Georgi's book on group theory and I came across this sentence..." Hilbert space of any parity invariant system can be decomposed into states that behave like irreducible representations". ...
2
votes
1answer
31 views

Is there a sensible fully-discretized Hamilton's principle?

In computational physics it is common to formulate Hamilton's principle in a semi-discrete way, where space is continuous but time is discrete: in other words the Lagrangian $$L(q, \dot q, t): ...
1
vote
1answer
139 views

Symmetries in QM and QFT — operator transformation laws

In quantum mechanics, we implement transformations by operators $U$ that map the state $|\psi\rangle$ to the state $U|\psi\rangle$. Alternatively, we could transfer the action of $U$ onto our ...
13
votes
3answers
1k views

Why is the Symmetry Group for the Electroweak force $SU(2) \times U(1)$ and not $U(2)$?

Let me first say that I'm a layman who's trying to understand group theory and gauge theory, so excuse me if my question doesn't make sense. Before symmetry breaking, the Electroweak force has 4 ...
3
votes
1answer
345 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
4
votes
10answers
1k views

Why does it take a projectile as long to get to its apex as it does to hit the ground?

I was once asked the following question by a student I was tutoring; and I was stumped by it: When one throws a stone why does it take the same amount of time for a stone to rise to its peak and then ...
8
votes
1answer
293 views

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 ...
0
votes
0answers
29 views

Any importance of $i$ before the time reversal operator for spin-1/2 system?

I've read about that: For systems with spin 1/2, time-reversal symmetry has the operator $\mathcal{T}=i\sigma_y K$. I wonder if the imaginary unit $i$ has any importance. Without $i$, ...
0
votes
1answer
41 views

Does invariance under infinite small transformation imply invariance to the finite one?

Let's say that I have finite chiral transform and I would like to show invariance of Dirac's Lagrangian when $m=0$ under it. The chiral transform is defined as: $$\psi(x) \rightarrow \psi'(x) =e^{i ...
5
votes
0answers
60 views

Intuition for S-duality

first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand ...
10
votes
2answers
571 views

How are anyons possible?

If $|ψ\rangle$ is the state of a system of two indistinguishable particles, then we have an exchange operator $P$ which switches the states of the two particles. Since the two particles are ...
5
votes
1answer
41 views

Why is a hexagon such a stable shape for materials?

A hexagonal lattice is famously the shape of graphene, the source of the 2010 Nobel prize. The shape also shows up in beehives and in the basalt columns of Giant's Causeway in County Antrim. ...
8
votes
2answers
332 views

Does Noether's theorem also give rise to quantities conserved over space?

Noether's theorem gives rise to quantities that are conserved over time. But does it also give rise to quantities that are conserved over space?
1
vote
1answer
32 views

Conserved current in a complex relativistic scalar field

For my field theory class I have the following Lagrangian density $$\mathscr{L}=\frac{1}{2}\eta^{\mu\nu}\partial_\mu\phi^*\partial_\nu\phi-\frac{1}{2}m^2\phi^*\phi$$ Where $\eta^{\mu\nu}$ is the ...
0
votes
1answer
27 views

Fine Structure Correction

The fine structure correction is composed of the relativistic correction and spin-orbit coupling. The lowest-order relativistic correction to the Hamiltonian is $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
0
votes
0answers
39 views

Laplace's demon and spontaneous symmetry breaking

One interpretation of Quantum mechanics is the hidden variable theory. This suggests that if we were to have a complete knowledge of the system at one time then the future states of the system are ...
3
votes
2answers
115 views

Is internal symmetry the same as gauge symmetry?

This is more a terminology question. I have seen that some people differentiate between the two types of symmetry: internal symmetry and gauge symmetry (of a field theory). Is there a difference (in ...
3
votes
1answer
775 views

Can conservation of momentum be violated?

The law of the conservation of momentum was accepted for year-hundreds. Even in Quantum field theory every particle collision must be momentum-conserving if there is homogenity in space. Can this ...
22
votes
6answers
2k views

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 ...
1
vote
1answer
59 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, ...
0
votes
0answers
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?
0
votes
0answers
23 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 ...
7
votes
1answer
97 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 ...
1
vote
1answer
51 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 ...
4
votes
1answer
96 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 ...
2
votes
1answer
64 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 ...
2
votes
1answer
31 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 ...
1
vote
0answers
87 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 ...
1
vote
1answer
61 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\\ ...
0
votes
1answer
34 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
votes
1answer
46 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 ...
5
votes
1answer
177 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 ...
8
votes
1answer
246 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 ...
3
votes
0answers
41 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 ...