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

0
votes
0answers
23 views

Symmetry Group of system to a given Hamiltonian

I want to determine the symmetry group of the following system: I consider a charged particle in a spherically symmetric potential $V$ and a homogeneous electric field of magnitude $E$ in ...
1
vote
0answers
31 views

Finding conserved quantities from Hamiltonian when Symmetry is not evident [on hold]

A particle is moving in 3D space, under a potential $$V = -\frac{\alpha}{r}-\frac{\vec{r} \cdot \vec{\mu}}{r^3 } $$ where $\vec{\mu}$ is some constant vector. I need to show there are three ...
1
vote
1answer
100 views

Classical action of the simple harmonic oscillator

I have been calculating the classical action of the harmonic oscillator, the problem I have is that I am only able to solve it if I set the integration limits of the action integral to be $t=T$ and ...
0
votes
0answers
22 views

Can we use combined symmetry to simplify the calculation of algebraic PSGs?

In classifying mean-field spin liquids under projective construction, the algebraic projective symmetry group (PSG) approach focus on the mathematical construction of the possible extensions of the ...
2
votes
1answer
32 views

Charge density and space inversion

J. D. Jackson in his book Classical Electrodynamics on page 249 ff. discusses the behaviour of electromagnetic quantities under space inversion (parity operation) and time reversal. He remarks: ...
2
votes
0answers
20 views

Bulk Symmetry corresponding to Yangian Symmetry of Planar N=4?

4D N=4 Super Yang Mills in the planar limit has an infinite dimensional symmetry known as Yangian symmetry. Dualities respect symmetries, so what does this symmetry correspond to in the $AdS_5\times ...
1
vote
0answers
49 views

Derivation of correction to canonical stress energy tensor due to addition of total divergence to Lagrangian

It is mentioned in almost every text book that equations of motions are not modified if we add a total divergence of some vector $$\partial_\mu \ X^{\mu}$$ to Lagrangian but canonical stress energy ...
2
votes
2answers
107 views

Why isn't our universe symmetric?

Why were random variations introduced in the spherically symmetric universe after Big Bang which made it non-symmetrical. Since the outcome of a coin toss depend on factors such as torque applied, air ...
7
votes
2answers
138 views

Dirac spinors under Parity transformation or what do the Weyl spinors in a Dirac spinor really stand for?

My problem is understanding the transformation behaviour of a Dirac spinor (in the Weyl basis) under parity transformations. The standard textbook answer is $$\Psi^P = \gamma_0 \Psi = ...
6
votes
2answers
163 views

How can we differentiate between matter and antimatter? [duplicate]

For instance if there was a galaxy, assume it to be made up of antimatter (isolated from other "normal" galaxies), how would we, or rather, would we be able to distinguish if it was made up of matter ...
2
votes
0answers
24 views

What symmetry operation mixes states with different $\ell$ in hydrogen atom? [duplicate]

We can mix states with different $m$ in hydrogen atom by rotating it around some axis (not coinciding with $z$). Thus rotation is the symmetry operation which mixes states with different $m$. As ...
3
votes
1answer
40 views

Solution space of a differential equation with 3D rotational symmetry

We know that the space of solutions will be invariant under 3D rotations, but why can we say that the space of solutions will constitute a representation of the rotation group $SO(3)$? We know that a ...
2
votes
1answer
47 views

Choice of the z-axis in the Schrödinger equation for the hydrogen atom

I am reading about the solution of the Schrödinger equation for the hydrogen atom and have a question about the choice of the z-axis. Most websites say that the z-axis is arbitrarily chosen. If so, ...
2
votes
0answers
79 views

Symmetry, gauge, and projective symmetry group (PSG)?

My following questions come from the understanding of the relations between the PSGs for two gauge-equivalent mean-field (MF) Hamiltonians (or MF ansatz). Considering the Schwinger-fermion ...
0
votes
1answer
102 views

How to know if the pseudoscalar Yukawa Lagrangian is invariant under chiral transformation?

The pseudo-scalar Yukawa theory Lagrangian is $$\mathcal{L}=\bar{\psi}(i\gamma ^\mu \partial_\mu - m)\psi -g\bar{\psi}i\gamma^5\phi\psi,$$ where $g$ is a coupling constant. How can I show it is ...
7
votes
1answer
159 views

Invariance of action $\Rightarrow$ covariance of field equations?

Invariance of action $\Rightarrow$ covariance of field equations? Is this statement true? I have only seen examples of this, like the invariance of Electromagnetic action under Lorentz ...
0
votes
1answer
36 views

Complex scalar field

In his book on Quantum Field Theory, Ryder mentioned in p. 91 under the title Complex Scalar Fields and Electromagnetism, the following: He said that under a global phase transformation $$\phi ...
2
votes
0answers
88 views

Para and ortho hydrogen angular momentum values

In Wikipedia, it is said that: Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons. ...
3
votes
1answer
115 views

Is General Relativity based on a Symmetry?

In short: Is there any kind of symmetry one can start with to derive general relativity (GR)? Longer: Einstein had the opinion that GR was the generalisation of special relativity, because instead of ...
4
votes
3answers
93 views

Spontaneous symmetry breaking to subspace not giving massless bosons

I'm currently trying to understand spontaneously broken in general and have stumbled upon a weird result which doesn't seem to correspond to my knowledge about broken gauge symmetries. Suppose we ...
4
votes
1answer
314 views

Angular momentum in curved spacetime

It is known that the angular momentum components are also a representation of the $SU(2)$ generators. Given a non-trivial spacetime, say a black hole of some kind or AdS space, how can one define the ...
5
votes
1answer
66 views

Symmetries of AdS$_3$, $SO(2,2)$ and $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$

Basically, I want to know how one can see the $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ symmetry of AdS$_3$ explicitly. AdS$_3$ can be defined as hyperboloid in $\mathbb{R}^{2,2}$ as $$ ...
2
votes
1answer
37 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
0answers
53 views

Simple questions on the symmetric eigenstate and time-reversal (TR) breaking eigenstate?

Followings are two independent questions as implied by the title: (1) Considering a quantum Hamiltonian $H$ possesses some symmetries described by a symmetry group $G=\left \{ g_1,g_2,...,g_n \right ...
1
vote
0answers
22 views

Conductivity Matrix (Symmetry Information)

I'm trying to understand the symmetry content of the conductivity matrix: one information is, presence of time-reversal symmetry causes the off-diagonal terms to vanish. When this is broken (e.g. in ...
2
votes
0answers
32 views

Discrete Symmetries: Breaking and Preserving

This is not a question, let's list down all the effects resulting from breaking or preserving of various discrete symmetries, on various observables, be it in condensed matter or in high energy. ...
0
votes
0answers
19 views

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: ...
1
vote
1answer
73 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
80 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 ...
1
vote
0answers
17 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 ...
3
votes
1answer
217 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 ...
2
votes
0answers
45 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 ...
1
vote
1answer
45 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
votes
1answer
163 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 ...
9
votes
1answer
104 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 ...
8
votes
3answers
88 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
102 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
56 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
23 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
52 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 ...
4
votes
1answer
105 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 ...
0
votes
0answers
15 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
79 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 ...
1
vote
1answer
99 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
69 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 ...
7
votes
2answers
115 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
0answers
40 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
55 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
43 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
137 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 ...