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

7
votes
0answers
56 views
+100

Highest symmetric non-maximally symmetric spacetime

What is the highest number of symmetries (Killing vectors) that a (4-dimensional) spacetime can have without being maximally symmetric? From what I can see, it seems to be 7 (which includes the ...
4
votes
1answer
23 views

Why exactly do sometimes universal covers, and sometimes central extensions feature in the application of a symmetry group to quantum physics?

There seem to be two different things one must consider when representing a symmetry group in quantum mechanics: The universal cover: For instance, when representing the rotation group ...
7
votes
4answers
178 views

What role does “spontaneously symmetry breaking” played in the “Higgs Mechanism”?

In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
7
votes
3answers
2k views

Definitions and usage of Covariant, Form-invariant & Invariant?

Just wondering about the definitions and usage of these three terms. To my understanding so far, "covariant" and "form-invariant" are used when referring to physical laws, and these words are ...
2
votes
1answer
57 views

Difference between symmetry and invariance

I'm wondering what's the real difference between symmetry and invariance in Physics? I believe that sometimes the two words are given the same meaning and some other times they are used in a different ...
2
votes
0answers
67 views

Symmetry in quantum mechanics

I originally asked this on the maths site, but I'll repost it here. Let $\mathcal{H}$ be the separable Hilbert space associated to some quantum system, and let $\langle\cdot,\cdot\rangle ...
3
votes
3answers
129 views

Scalar and vector defined by transformation properties

In Classical Mechanics, we are defining scalars as objects that are invariant under any coordinate transformation. Vectors are defined as objects that can be transformed by some transformation matrix ...
11
votes
4answers
3k views

Symmetry in resistor circuits

Given 6 points that are connected with each other with a resistor of resistance $R$, find the resistance between any two points. (Answer: $R/3$) (All the conducting wires have the same ...
-1
votes
0answers
39 views

Why the Yang-Mills ansatz is able to describe every interaction we know? [on hold]

All interactions which seem to rule the microscopic world we have access to are described by the standard model, which is a Yang-Mills theory for the SU(2) x SU(3) x U(1) group. Also, gravity can be ...
5
votes
2answers
70 views

Conservation Laws and Symmtery

The toughest of topics in physics, like Quantum Mechanics, Relativity, String theory, can be explained in layman words and many have done so. Though there is no substitute to the understanding a ...
9
votes
3answers
290 views

What is the exact meaning of homogeneity in cosmology?

I understand that, in general, homogeneity is the physical attribute of being uniform in composition (" of the same form at every point"), but I'm slightly confused when it is used in cosmology as ...
1
vote
1answer
32 views

Identical particles: Why only two possibilities?

Given two identical particles, Wikipedia says that the wavefunction of a combined system where the first particle is in state $|n_1\rangle$ and the other one is in $|n_2\rangle$ is ...
28
votes
2answers
3k views

Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or points of view: Anomalies are due to the fact that quantum field ...
0
votes
1answer
71 views

In field theory, why are some symmetry transformations applied to the field values while other act on the space that the fields are defined on?

My basic understanding is that a field theory consists of symmetry groups, a space $S$ that the symmetry groups act on and of fields defined on that space $S$. In other words, the space $S$ is the ...
1
vote
1answer
118 views

Symmetry arguments for valley physics in graphene with broken inversion

I am trying to understand this paper: http://link.aps.org/doi/10.1103/PhysRevLett.99.236809 (Here is an arXiv version: http://arxiv.org/abs/0709.1274) In the introduction, they mention certain ...
5
votes
2answers
54 views

Is there a proof that space expanding produces observers at all points that see what we see?

I know that galaxies are moving away from us, and so can see that it's intuitive that if space was expanding, then the astronomical observations from Earth would be the same as at all other points in ...
1
vote
1answer
124 views

Is my understanding of Gauge Symmetries correct?

I'm currently working on a project about Symmetry Breaking for my physics bachelor. Right now I'm trying to understand Gauge Symmetries (although I guess it's not much of a symmetry). And I've been ...
1
vote
1answer
146 views

Point group symmetries and unit cell

I was wondering if the unit cell (of a given lattice) had to have every point group symmetries of the lattice it defines ? I guess there is no unique way to define a unit cell and that it may not have ...
0
votes
5answers
44 views

Flux of $E$ through the shaded side

A charge $q$ sits at the back corner of a cube, as shown in Figure. What is the flux of $E$ through the shaded side? One of the solution stated that. Looking at the figure, we notice two ...
9
votes
1answer
352 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 ...
3
votes
1answer
73 views

Permutation symmetry - a continuous symmetry?

From quantum mechanics it is known that permutation between identical particles does not change the Hamiltonian. Assuming that the quantum system consists of a very high number of particles such that ...
4
votes
3answers
10k views

What is difference between homogeneous vs isotropic material?

When we say a material is isotropic? When properties such as density, Young's modulus etc. are same in all directions. If these properties are direction dependent, then we can say that the material is ...
0
votes
0answers
19 views

Using the Mirror Rule to determine the magnetic field of an infinite slab

Consider a slab infinite in the y and z direction but with finite width W in the x direction. Current flows in the (+y) direction. I'm supposed to use the "mirror rule" to show that at a point in the ...
4
votes
0answers
162 views

Why does physics have so many symmetries?

I have just found out that in order to modify mass in his special theory of relativity, Einstein assumed that energy and momentum are always conserved.$^\dagger$ I think surely there are other ways to ...
4
votes
0answers
86 views

Why does Wikipedia equate hidden symmetry with broken symmetry for the standard model?

I have recently started studying the basic ideas of symmetry and group representation in order to understand the basic principles behind the standard model. I do follow the difference between a global ...
0
votes
1answer
126 views

Finite potential well, parity of solutions

I'm working through some problems for a QM exam and I've realised I don't really understand the concept of parity of solutions. I'm looking at a simple finite potential well problem: $$V(x)=0, \quad ...
9
votes
5answers
401 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
1answer
55 views

Representation of U(1) on fock space

I am currently reading up on the use of group theory in physics using Peter Woit's book draft (available on his homepage). I do understand the mathematical concepts but have a bit of a problem making ...
2
votes
2answers
302 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 ...
5
votes
5answers
328 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
0answers
713 views

What is the definition of particle-hole symmetry in condensed matter physics?

People often talk about particle-hole symmetry in solid state physics. What are the exact definition and physics picture of particle-hole symmetry? How to define the density of particles and holes?
1
vote
1answer
68 views

Canonical spinors from gauge transformations

In this 2006 paper, http://arxiv.org/abs/hep-th/0610128, there is the concept of gauge transformation and how was it employed that I do not fully understand. Note, what will be talked about below is ...
1
vote
1answer
46 views

What is meant by invariant under change of coordinates **to first order**?

I am studying elementary Lagrangian mechanics, and I'm a bit confused about the what's meant by invariance of the Lagrangian under change of coordinates to first order. More specifically, Noether's ...
0
votes
0answers
55 views

Parity of $n$-photon system

The $C$-parity (charge conjugation) of an $n$-photon system is given by $(-1)^n$. If I'm not totally wrong, the intrinsic parity of a photon is $(-1)$. What is the parity $P$ of a system of $n$ ...
1
vote
3answers
88 views

Formulating the Lagrangian in terms of invariant quantities

Consider a closed system consisting of $N$ point particles, whose Lagrangian is given in the standard way, by the total kinetic energy minus the potential energy: $\mathcal{L}(\dot{q},q):= T(\dot{q}) ...
2
votes
0answers
40 views

How is translational symmetry related to Fourier decomposition?

The book (The Cosmic Microwave Background By Ruth Durrer) about cosmological perturbations says that because of translational symmetry of the background at a constant time, we can decompose our ...
3
votes
2answers
82 views

Noether's theorem: meaning of transformation of coordinates

I have a question regarding Noether's theorem. In our introductory QFT class (which is based on the book by Michele Maggiore) we have derived the Noether currents in the same form as displayed in this ...
1
vote
1answer
32 views

Are the mass matrices the same if Higgs corresponding to different Cartan generators get a vev?

I'm trying to understand what happens when a Higgs field in the adjoint representation of a given gauge group gets a vacuum expecation value (vev). Normally, the fermions do not couple to adjoint ...
9
votes
2answers
975 views

Why is the stress-energy tensor symmetric?

The relativistic stress-energy tensor $T$ is important in both special and general relativity. Why is it symmetric, with $T_{\mu\nu}=T_{\nu\mu}$? As a secondary question, how does this relate to the ...
1
vote
1answer
62 views

Hermitian conjugate of an antiunitary transformation

In quantum mechanics, one often considers symmetry transformations which are defined in terms of operators which do not change the norm of states in the Hilbert space. For the Wigner's theorem, this ...
4
votes
0answers
39 views

Target Space Lorentz Invariance vs. World Sheet Weyl Invariance

The Polyakov action, $S\sim \int d^2\sigma\sqrt{\gamma}\, \gamma_{ab}\partial^a X^\mu \partial ^b X_\mu$, has the well known classical symmetries of world sheet diffeomorphism invariance, world ...
1
vote
1answer
470 views

Lack of symmetry of the canonical stress-energy tensor

Why in the general case of classical field theory canonical stress-energy tensor doesn't have symmetry of the permutation of the indices? For explanation, let's have a "derivation" of an expression ...
2
votes
1answer
60 views

From Noether's theorem to canonical Energy-Momentum tensor using translations

In this text that I am reading it says that the transformation $\delta \phi(x)$ is a symmetry if the Lagrangian changes by a total derivative: $$\delta \mathcal{L}= \partial_{\mu}F^{\mu} . $$ From ...
0
votes
0answers
39 views

Resource for (String) Symmetry Breaking in Terms of Roots and Weights?

I'm currently searching, for quite a while now, for a paper/book that discusses symmetry breaking in terms of roots and weights. Any suggestions would be much appreciated!
1
vote
1answer
31 views

How can crystal symmetry operations be used to reduce the number of unique properties of a solid?

Can anyone please give an example or a reference which shows how crystal point groups and symmetry operations can be used to reduce the number of parameters describing the property of a crystal, ...
0
votes
4answers
96 views

Why, when and where is Gauss's law applicable?

Why is it said that Gauss's Law is mainly applicable for symmetric surfaces/bodies? Why not for asymmetric surfaces? I want a logical explanation! BTW my teacher said that Gauss's law is ...
3
votes
2answers
155 views

Ricci flat compact manifold with $U(1)\times{}SU(2)\times{}SU(3)$ isometry group?

As the title says, is it possible to have a Riemannian Ricci flat compact manifold with $U(1)\times{}SU(2)\times{}SU(3) $ isometry group?
2
votes
1answer
215 views

Does Noether's theorem apply to entropy?

Entropy appears to have a translation symmetry - adding some constant value to it doesn't appear to my fairly rudimentary understanding of physics alter the actual physics. Is this correct? Now ...
1
vote
3answers
876 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 ...
3
votes
1answer
176 views

What does Lee Smolin mean when he says that the most fundamental theory can have no symmetries?

Quote from Lee Smolin in Scientific American: There are some lazy ideas about unification that reflect uncritical thinking, such as the idea that the more fundamental a phenomena [sic] is the more ...