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

1
vote
1answer
58 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 ...
2
votes
1answer
60 views

Landau's Problem - Poisson bracks of a spherical symmetry function and angular momuntum in z axis

In landau's Mechanics, there's a problem: I think, if the function has the property spherical symmetry, or: $\phi(r,p)=\phi(-r,-p)$ The form suggested by Landau follows this property, but I can't ...
2
votes
2answers
171 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 ...
1
vote
0answers
15 views

Can an axisymmetric solution produce antisymmetric eigenfunctions?

I'm solving a vibrating membrane. In order to simplify my calculations, it's tempting to assume axisymmetric behaviour. If I solve an axisymmetric problem, am I going to lose all the antisymmetric ...
4
votes
1answer
225 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 ...
8
votes
2answers
145 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 ...
3
votes
1answer
207 views

Which transformations *aren't* symmetries of a Lagrangian?

As far as I understand, Noether's theorem for fields works, as explained in David Tong's QFT lecture notes (page 14) for example, by saying that a transformation $\phi(x) \mapsto \phi(x) + \delta \phi ...
4
votes
1answer
136 views

Why is Planck's constant the same for all particles?

This question came to me while reading "Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?". This question has a nice answer that explains that wave number has be ...
2
votes
0answers
36 views

Consequences of Entropy/Information Reversal in a System?

Can pairs of different physical systems be symmetrical under a process which would turn one of these physical system's entropic and informational contents into another system's respective ...
6
votes
3answers
162 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 ...
1
vote
0answers
20 views

What are spin and valley symmetries in graphene?

I have been assigned a presentation on a part of a paper ( http://arxiv.org/ftp/arxiv/papers/1303/1303.6942.pdf ). My task is to present on the spin and valley symmetries in graphene, and relate it ...
1
vote
0answers
13 views

Visualisation of representations and their decomposition into irreps [migrated]

A question in a Representation Theory midterm got me thinking, and made me realise I didn't really understand irreps. The question was on the subject of reps of $S_4$, and went: An obvious ...
7
votes
0answers
52 views

Confusion about two definitions of anomalies

As I am currently studying for an exam about quantum field theory and string theory, I got confused about the notion of "anomalies" and how they are actually defined. Similar questions have already ...
3
votes
2answers
199 views

A kind of Noether's theorem for the Hamiltonian

How can I (conveniently?) show that an invariance of the Lagrangian and Hamiltonian (i.e. the kinetic as well as the potential energy are independently invariant) will lead to a conservation law using ...
3
votes
1answer
163 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 ...
8
votes
3answers
61 views

When do phase space functions' Poisson brackets inherit the Lie algebra structure of a symmetry?

I've seen several examples of phase space functions whose Poisson brackets (or Dirac brackets) have the same algebra as the Lie algebra of some symmetry. For example, for plain old particle motion in ...
1
vote
1answer
67 views

Normal modes of two parallel $LC$ oscillators coupled via mutual inductance

Consider the circuit shown below. The two LC circuits are arranged in such a way that their mutual inductance M results in a coupling between the currents flowing in the two circuits. Find the ...
1
vote
0answers
41 views

Why doesn't Graphene have a band gap?

Is there any simple justification about graphene having no band gap? How bout its linear E-K? Why bilayer graphene has a quadratic E-K and electric field can open a band gap there? I do not ...
2
votes
0answers
21 views

What is the the real world interpretation of the high dimensionality of quasicrystals?

One of the examples of the problems of 5-fold symmetry is that pentagons tiled on a 2D plane do not completely fill that plane, leaving voids. This may be solved by "folding" it into 3D space, and ...
0
votes
0answers
42 views

Conservation of kinetic energy on a moving inertial frame

The velocity of an object differs from the point of views of two different inertial observers standing at two different frame of reference. Assuming no gravity and acceleration = 0 for the object and ...
1
vote
1answer
130 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 ...
3
votes
1answer
81 views

Connection between conserved charge and the generator of a symmetry

I'm trying to understand the connection between Noether charges and symmetry generators a little better. In Schwartz QFT book, chapter 28.2, he states that the Noether charge $Q$ generates the ...
5
votes
1answer
235 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
13 views

Symmetry of amorphous thin films

I'm wondering whether amorphous thin films have point group symmetries? Landau's Statistical Physics Vol. I writes: The highest symmetry is that of isotropic bodies (bodies whose properties are the ...
2
votes
1answer
70 views

Derivation of Baryon Number conservation?

The symmetry connected to Baryon/Lepton Number conservation is, as far as I understand, global U(1) symmetry (which is called here global gauge invariance). Does anyone know of an explicit ...
7
votes
2answers
113 views

Why are these two definitions for symmetries in the Lagrangian equivalent?

I have heard the following two definitions for a symmetry of the Lagrangian: If under a coordinate transformation the form of the Lagrangian remains unchanged then there is a symmetry. If $\delta ...
1
vote
1answer
72 views

Using Ampere's Law without Right-Hand-Rule to derive an expression for the magnetic field around a current

I'm a little confused over the textbook example of applying Amperians to get the magnetic field around a current. I understand we take a loop which shares the rotational symmetry of the wire (a ...
1
vote
1answer
56 views

Convenient coordinate systems and symmetries

I recall in my basic electromagnetism and quantum mechanics lectures that choosing one coordinate system over another may greatly simplify the equations involved in solving a problem (think about ...
1
vote
0answers
35 views

Laplace's equation with spherical, cylindrical, and planar symmetry [closed]

Find the general solution to Laplace's equation for spherical symmetry (everything can only depend on $r$, the radius), cylindrical symmetry (everything can only depend on $s$, the radius), and ...
1
vote
0answers
53 views

Nature favours symmetry?

In my chemistry class today, our professor was giving a lecture on symmetry of organic molecules. He said that " Nature favours symmetry as symmetry reduces the energy of the system". But as far as ...
2
votes
0answers
35 views

Explicit degeneracy in SPT phases

In the wikipedia article on symmetry protected topological phases the author states: If the boundary is a gapped degenerate state, the degeneracy may be caused by spontaneous symmetry breaking ...
1
vote
1answer
64 views

Can someone explain LO-TO Splitting?

LO-TO splitting occurs in an ionic (i.e. polar) solid such as GaAs or NaCl. What happens is that the degeneracy of the transverse optical (TO) and longitudinal optical (LO) phonons at $k=0$ is broken ...
0
votes
1answer
65 views

Rotational symmetry in integration

Can someone please tell me why $$4\int d^4x \, x^\mu x^\nu ~=~\int d^4x \, g^{\mu\nu}x^2 $$ by some rotational symmetry argument?
0
votes
2answers
102 views

Lorentz symmetry and Noether's theorem

I'm trying to overcome some misunderstanding that I have in Noether's theorem. There is formula in David Gross's Lectures on QFT for Noether's theorem: ...
3
votes
2answers
80 views

Particle number conservation equals $U(1)$-symmetry?

If have by now frequently read the above but never really understood it. It is said that the particle number conservations is related to the phase of the wave function, but how?
0
votes
1answer
62 views

Notation in the book Symmetry by Hermann Weyl

I'm having troubles understanding a notation of the symmetry groups in a book "Symmetry" by Hermann Weyl. On the page 80 of the 1952 Princeton University Press edition of the book, Weyl lists the ...
1
vote
1answer
79 views

Why three families of multipole moments?

There are three families of multipole moments: The electric multipole moments, the magnetic multipole moments and the toroidal multipole moments. Is there any reason why there are this three families ...
0
votes
1answer
38 views

Conserved current for a constant translation of a free massless scalar field

In Zinn-Justin's Quantum Field Theory and Critical Phenomena they start with an action for a free massless scalar field: $$S(\varphi) = \frac{1}{2}\int ...
4
votes
0answers
66 views

Can you gauge a $U(1)_L$ symmetry?

I recently calculating the one loop correction for the propagator of a gauge boson, $\hspace{5cm}$ I assumed arbitrary left and right couplings, $ g _L $ and $ g _R $. I found that the one loop ...
6
votes
1answer
137 views

Spontaneous symmetry breaking and time-reversal symmetry

In most textbooks on field theory you read that "spontaneous symmetry breaking implies degeneracy of the ground state". (Like for example in ...
3
votes
1answer
71 views

Bondi-Metzner-Sachs (BMS) symmetry of asymptotically flat space-times

I started studying the BMS symmetry in connection with the paper: http://arxiv.org/abs/1312.2229 and there are a few strange things I noticed. First of all, from reading the original papers by Bondi, ...
15
votes
5answers
802 views

When is it useful to distinguish between vectors and pseudovectors in experimental & theoretical physics?

My understanding of pseudovectors vs vectors is pretty basic. Both transform in the same way under a rotation, but differently upon reflection. I might even be able to summarize that using an ...
2
votes
2answers
100 views

Doubt regarding Ampere's Circuital Law

The Ampere's Circuital law states $$\oint B\cdot d\ell~=~ \mu_0I$$ We can use it to derive the magnetic field of an infinitely long current carrying wire easily. My question is, why does the wire ...
4
votes
1answer
110 views

Crystal Momentum in a Periodic Potential

I'm working through some basic theory on periodic potentials, and I would appreciate help in understanding the crystal momentum. Suppose we have a Bravais lattice with lattice vectors $\textbf{R}$. ...
2
votes
1answer
42 views

Deriving conserved currents by promoting parameter

I currently reading Tong's text on String Theory. In Chapter 4.1.1 he alludes to a technique to derive conserved currents Recall that we can usually derive conserved currents by promoting the ...
2
votes
0answers
69 views

Symmetry and Algebra

I'm trying to get a more concrete idea how symmetry is understood in quantum theories, as broad as possible. Consider a infinitesimal transformation of states in quantum physics of the form: $$ ...
2
votes
0answers
41 views

Examples of manifolds (not) being: flat, homogeneous and isotropic

I am looking for (at least) one example of the following manifolds: Flat, homogeneous and isotropic Curved, homogeneous and isotropic Flat, non-homogeneous and isotropic Flat, homogeneous and ...
4
votes
4answers
148 views

Why do we look at the representations of $SO(3)$ in QM?

I have a bit of an understanding issue why the representations of $SO(3)$ are so important for Quantum Mechanics. When looking at its Irreps one gets the Spin and Angular Momentum operators and thus ...
1
vote
1answer
83 views

The role of SO(3) and SU(2) in quantum mechanics [duplicate]

When studying the irreducible representations of SO(3) one usually looks at the irreps of the infinitesimal rotations instead, i.e. the ones of so(3), the Lie Algebra of SO(3). The Irreps of so(3) can ...
1
vote
1answer
44 views

Symmetric eigenfunctions?

So a symmetric eigenfunction / wavefunction is defined as: $$P_{ij} ψ_a (r_1,r_2,…,r_i,…,r_j,…,r_N )=ψ_a(r_1,r_2,…,r_i,…,r_j,…,r_N )$$ But for it to be symmetric does this have to be true for all $ij$ ...