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
40 views

Questions on the derivation of the Lorentz transform

I began trying to understand how special relativity was developed by reading this. Although the proof is very simplistic and probably gives a somewhat shallow understanding of the theory; it is the ...
9
votes
1answer
644 views

Confusion in a trick in solving an energy eigenfunction

Given a non-relativistic energy eigenfunction for a central potential $\left|\Phi \right>$ In solving relativistic hydrogen atom, one of the terms is $$ \left<\Phi\middle|\frac{e^2}{r}\middle|\...
27
votes
4answers
5k views

Are black holes perfect spheroids?

What I know about black holes (correct me if I'm wrong) is that they are the most compact objects in the universe that have been discovered. Due to all that gravity, wouldn't black holes be a perfect ...
2
votes
2answers
84 views

Two particles system

Source: this video For a system with two particles (09:30), why is its wave function a product of each particle's wave function? E.g. $$\psi(x_1,x_2)=\psi_a(x_1)\psi_b(x_2)$$ For indistinguishable ...
2
votes
0answers
24 views

Sublattice symmetry vs Particle hole symmetry

Sublattice symmetry and particle hole symmetry generally constrain a system's energy spectrum to be symmetric with respect to fermi level. My understanding is that they are both represented by an ...
2
votes
2answers
59 views

Why is the infinitesimal SUSY variation generated by the sum of a left- and right-chiral generator

I was wondering why in many (all? e.g.https://arxiv.org/abs/hep-ph/9709356) resources on N=1 SUSY the variation of a field in the simplest free susy model is defined as $$\delta_\epsilon \phi = (\...
-1
votes
0answers
28 views

Angular Momentum of Closed Subshell

Suppose we have a state with $2\ell +1$ fermions all entirely in the subspace of hydrogen eigenfunctions with $n, \ell$ fixed. That is we have a state occupied by $2\ell +1$ fermions involving $\mid \...
0
votes
0answers
39 views

Confusion about symmetry factor

I have some questions about symmetry factor. When we count symmetry factor, we count something like how to permute propagators in Feynman diagram, but I think this counting is already taken care of by ...
-1
votes
0answers
27 views

Symmetries in quantum systems - Wigner theorem and commutation with Hamiltonian

I was reading about symmetries in quantum systems and found (at least) two different definitions. According to Wigner's theorem symmetry transformation (of a quantum system) is a bijective map between ...
2
votes
2answers
228 views

Symmetries of non-parallel infinite conducting planes

Suppose I have semi-infinite conducting planes that intersect at some angle $\theta_0$ and have a potential difference of $V$ (the axis of intersection is somehow insulated so they are not actually in ...
0
votes
0answers
49 views

Matching symmetry factor when a heavy vector field is integrated out

Let us consider the lagrangian $$ \mathcal{L} = \alpha \bar{u}\gamma^\mu u V_\mu + \frac{\beta^2}{2}V_\mu V^\mu $$ there $V_\mu$ is a heavy vector field and $u$ is a massless SU(3)-colored quark. If ...
0
votes
3answers
56 views

Could dark matter possibly be anti-matter?

Considering the broken symmetry after the big bang - what I understand as there being a huge surplus of matter and a lesser presence of anti matter - is it possible that dark matter could be anti-...
5
votes
3answers
63 views

Why is there a matter-dark matter asymmetry?

It is said generally that nature is symmetric. For example if light behaves as both a particle and a wave, then matter must also do so, which turns out to be true. But we find that the Universe ...
-1
votes
0answers
30 views

Hexagonal shape of snow flakes [duplicate]

As we know snowflakes has hexagonal shape. My question is why is that? and Is there any mathematical model which can explain that particular geometric shape of the snowflakes?
5
votes
1answer
57 views

Why does galilean invariance imply that particles that start rest stay on the same line?

I'm reading Arnol'd for self study. I'm struggling with this question: "Show that any system of two particles will remain on the same line that connected them at the initial moment, if they started at ...
1
vote
0answers
91 views

The Mechanism Behind Massless Particles Acting As One Massive Particle

I am reading a historical account of the development of the Higgs Field theory by Sean Carroll. In it, he states that the 1963 paper by Anderson postulated that "the massless Nambu-Goldstone bosons ...
1
vote
0answers
26 views

Can an azimuthally symmetric perturbation lift the 2l+1 degeneracy of angular momentum eigenstates?

Assume the initial Hamiltonian of a spinless, non relativistic particle is $$H_0(r,\theta,\phi)=\frac{{\bf p}^2}{2m}+V_0(r)$$ Such that the eigenstates are angular momentum eigenstates $|n,l,m>$, ...
0
votes
0answers
29 views

Why is charge conjugation multiplicative?

I'm reading Mann's book on the standard model and particle physics and he doesn't explain why C symmetry is multiplicative other than saying it's discrete which isn't very convincing to me. In ...
0
votes
1answer
51 views

What does it mean to say “internal symmetry”?

What does it mean to say "internal symmetry"? Let me try to express the way I see it, so you can have it as a starting point. There are spacetime symmetries, which are global since any Lorentz ...
0
votes
1answer
100 views

Is the Potential Energy just a bookkeeping device?

It is said that if the space is homogeneous then momentum is conserved. But I've been thinking in the following situation: Consider a parallel plates capacitor. In between the plates there is a ...
0
votes
1answer
40 views

Homogenity and Isotropicity of space

In school it is given that law of conservation of momentum is a result of homogeneity of space and law of conservation of angular momentum is a result of isotropicity of space but what is isotropicity ...
1
vote
0answers
32 views

Generalise Noether's theorem [closed]

I'm not sure how to generalise Noether's theorem. For this L, I think $B\cdot\dot{x}$ is conserved so I tried to relate F and K to this and try to show that that was conserved but got no where. any ...
2
votes
0answers
102 views

How to arrive at the Dirac Equation from Poincare Algebra?

For the case of Galilean group, the time translation is given by the generator $H$. Hence, $$\mid\psi(t)\rangle\to \mid\psi(t+s)\rangle =e^{-iHs}\mid\psi(t)\rangle$$ Which immediately is the ...
2
votes
1answer
76 views

Relationship between zero modes and symmetry in a simple system of coupled springs

This Wikipedia page states that "zero modes appear whenever a physical system possesses a certain symmetry," and gives the example of a ring of beads connected by springs having a zero mode associated ...
1
vote
1answer
37 views

Why are numbers not consistent? (Identifying phonon's frequency)

I am trying to connect several facts between each other to acquire a consistent picture. Fact 1. Monolayers of tungsten disulphide $WS_2$ have hexagonal crystal lattice, and the first Brillouin zone ...
0
votes
1answer
48 views

Lorentz transformation and symmetries of the Lagrangian [duplicate]

Since the Lagrangian of our quantum field theories is covariant under Lorentz transformations I'm asking myself if there is any link to some symmetries (like that we get from gauge transformations ...
0
votes
2answers
54 views

Energy of central potential in QM

A hydrogen atom (Coulomb potential) has energy that only depends on $n$ (if we ignore other effects like spin-orbit coupling). In general (not necessarily Coulomb, can be any V), does $E$ depend on ...
1
vote
1answer
35 views

What is the gravitational/electric/inverse-square field inside a cylinder?

I've read from the shell theorem that an inverse-square potential has zero field inside a spherical shell. What about the field inside a cylinder? Are objects inside a long cylinder attracted to the ...
1
vote
2answers
86 views

Prove energy conservation using Noether's theorem

I wonder how you prove that energy is conserved under a time translation using Noether's theorem. I've tried myself but without success. What I've come up with so far is that I start by inducing the ...
7
votes
2answers
257 views

Damped oscillator: time-reversal, time-translation and dissipation

The equation of motion of a damped oscillator $$\frac{d^2x}{dt^2}+\gamma\frac{dx}{dt}+\omega_0^2x=0$$ which is invariant under time-translation $t\rightarrow t+a$, but not under time reversal $t\...
0
votes
0answers
21 views

Implication of breakdown of scale invariance for problems with intrinsic length or time scales?

According to Wikipedia article on scale invarince, the equations for electric (and magnetic) fields : $$\nabla^2\vec{E}=\frac{1}{c^2}\frac{\partial^2\vec{E}}{\partial t^2}\hspace{0.3cm}\text{and}\...
1
vote
1answer
81 views

Why is quark flavor just a SU(N) group?

In the standard model one has U(1) for electromagnetism, SU(2) for the weak sector and SU(3) for the color sector. One could say that in the quark part of the fermions, there are $$ \underbrace{6}_\...
0
votes
0answers
36 views

A Question about a $U(1)_{B-L}$

I know I can write the QCD lagrangian like this: $$ \mathcal{L} = (i\bar{q}_{R} \gamma_{\mu}\partial_{\mu} {q}_{R} + i\bar{q}_{L}\gamma_{\mu}\partial_{\mu} {q}_{L}) + \text{other terms} $$ When ...
-1
votes
1answer
57 views

Understanding standard model and symmetry

I just want to know whether my understanding regarding standard model and symmetry is correct or utter nonsense. The standard model is the (yet incomplete) Lagrangian of the universe. The ...
2
votes
0answers
73 views

Analyzing the free-particle kernel [closed]

I recently began studying the theory of path integrals from the book by Feynman and Hibbs. The Problem $3.6$ asks to give an argument to show that $F(t_b,t_a)$ depends only on $t_b-t_a$. ...
3
votes
2answers
150 views

Physical difference between gauge symmetries and global symmetries

There are plenty of well-answered questions on Physics SE about the mathematical differences between gauge symmetries and global symmetries, such as this question. However I would like to understand ...
0
votes
1answer
91 views

Notations for high symmetry points in the 1st Brillouin zone

I am trying to understand how I should interpret the letters like Г,K,M,T etc., that are usually there in the electronic band structure diagrams. So, let's assume we have graphene with its hexagonal ...
2
votes
0answers
40 views

Antiunitary operators in the tenfold way

In the classification of free fermion systems in condensed matter, physicists usually divide the systems into ten symmetry classes, first discovered by Altland and Zirnbauer. In their classification, ...
3
votes
2answers
36 views

Standard-model flavor symmetry

If we consider the chiral Lagrangian after the spontaneous symmetry breaking, we have got fermion masses and Yukawa couplings to the physical Higgs boson. So it follows global symmetries in flavor ...
3
votes
0answers
141 views

Are symmetries of a degenerate ground-state manifold always broken?

If a Hamiltonian has a global symmetry and a degenerate ground state, then in the thermodynamic limit, the ground states $| \psi \rangle$ that are eigenstates of the symmetry operator typically become ...
2
votes
0answers
42 views

Kitaev chaing, time reversel symmetry, particle hole symmetry

I was wondering if the Kitaev chain has time reversal symmetry. I think it probably doesn't because by staking Kitaev chains it is possible to create a so called Chern insulator with propagating ...
0
votes
1answer
57 views

Inversion symmetry points of graphene

I have question about graphene. When you have the graphene lattice two types of atoms can be distinguished, let's call them type A and B.You can draw a unit cell that has the shape of a parallelogram....
1
vote
1answer
53 views

What are the assumptions behind the Lagrangian derivation of energy?

What are the assumptions behind the Lagrangian derivation of energy? I understand that we're searching for a function $L$ that describes a set of physics so that solving the energy minimization ...
1
vote
1answer
68 views

Crossing Symmetry in Bhabha scattering and Moller scattering

Given the amplitude for a particular process, it may be possible to obtain the amplitude for another similar process by a so called crossing symmetry. I know there is a $s \leftrightarrow u$ crossing ...
0
votes
0answers
27 views

Lorentz invariance & Noether theorem of classical ED

I want to check invariance of the action under Lorentz boosts for classical electrodynamics. The action is $$S = \int \mbox{d}^4x F_{\alpha \beta} F^{\alpha \beta} $$ I assumed that the fields ...
0
votes
0answers
17 views

Effect symmetry on points in momentum space

I have to study some material for a condensed matter physics course and cam across a passage that I don't understand. "In momentum space time reversal symmetry and particle hole symmetry only have ...
0
votes
0answers
25 views

effect of inversion symmetry on the bandstructure

I have a very general question, but I hope that someone can answer it. Can someone describe what the effect of inversion symmetry is on the bandstructure. (Or is there not a general effect?). ...
4
votes
1answer
111 views

What does it mean for a topological phase to be “symmetry protected”?

I have seen some very nice and enlightening awnsers to questions related to topological order and insulators, such as here, or here. However, I'm still puzzled by the concept of "symmetry protection" ...
0
votes
1answer
70 views

What is gate symmetry?

I just read this interesting interview with Frank Wilczek and he talks a couple of times about gate symmetry, without ever defining the term. This isn't a term I've come across, and google throws up ...
4
votes
1answer
71 views

Symmetries in physics (specifically condensed matter physics)

Symmetries play a big role in physics. Some symmetries are translation symmetry, rotation symmetry, time translation symmetry, timereversal symmetry etc. It seems that in condensed matter physics ...