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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Role of the crystallographic point group on properties of tensorial elasticity

If a space point group for a crystal is known, does this automatically define the elastic tensor symmetry of the material? What further implications can be found? The crystallographic subgroups: ...
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62 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 ...
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62 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 ...
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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 ...
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209 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 ...
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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 ...
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21 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 ...
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1answer
137 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 ...
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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 ...
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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 ...
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64 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 ...
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69 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 ...
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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 ...
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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 ...
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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 ...
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1answer
88 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
70 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 ...
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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?
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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: ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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112 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 $\textbf{R}$. ...
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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 ...
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1answer
72 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, ...
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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 ...
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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: $$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
84 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 ...
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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 ...
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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 $ij$ ...
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148 views

Quantum symmetries that are not classical symmetries

An anomaly is a symmetry of the classical action that fails to be a symmetry of the path integral, due to non-invariance of the path integral measure. Does it ever occur that the opposite thing ...
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82 views

Why is there a 'loophole' in Mermin Wagner for rotations?

I'm just starting out in my mathematics career by looking at some simple stuff on broken symmetries in statistical mechanics. Since 3D is 'hard' it would be very nice to look at 2D toy models of ...
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2answers
112 views

Could the universe have evolved WITHOUT the non-determinism of quantum mechanics? [closed]

(I'm going to make a few conjectures here - please answer the question in light of them as if they were true, even though of course they may be overly simplistic or wrong) Assuming that: the ...
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2answers
162 views

Do the standard cosmology models spontaneously break Lorentz symmetry?

In standard cosmology models (Friedmann equations which your favorite choice of DM and DE), there exists a frame in which the total momenta of any sufficiently large sphere, centered at any point in ...
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1answer
64 views

Time Energy symmetry in General Relativity (not asking about energy conservation)

In General Relativity is there a TE symmetry similar to CPT symmetry in the Standard Model ? It's pretty easy to understand that by flipping charge and parity you merely get a time reversed equivalent ...
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59 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 ...