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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How can one see that the Hydrogen atom has $SO(4)$ symmetry?

For solving hydrogen atom energy level by $SO(4)$ symmetry, where does the symmetry come from? How can one see it directly from the Hamiltonian?
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35 views

Gauss law question with regard to this example

I am really confused in Gauss law. Why do E3 and E2 pointing up? and also E1 pointing down? The lecture note said infer from symmetry and you will get the following but I dont really understand. ...
4
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4answers
209 views

Translational invariance implying diagonal representation in momentum space

I have just come across something in my reading of Peskin and Schroeder that claims that because a function, in this particular case a two-point correlation function, is translationally invariant, it ...
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1answer
36 views

The elementary particles uniformity and its limits in the context of matter [closed]

We know that matter particles are uniform, i.e. they are absolutely identical (1, 2, 3). Particles of various properties are uniform. But if we look at bigger matter elements, when and how does the ...
1
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1answer
98 views

Help on understanding a concept in Noether's first theorem

Given a Lie group $G$, whose most general transform depends on $\rho$ parameters, under the action of which an integral $I$ is invariant, there are $\rho$ linearly independent combinations of the ...
-1
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1answer
97 views

Galilean invariance/ scale invariance of KPZ

I have problems with understanding what the Galilean invariance of KPZ means and how it is connencted to KPZ scale invariance? How can I see that KPZ is scale invariant? Why this symmetry impose ...
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0answers
18 views

Discrete translational invariance of lattice systems and conserved quantities [duplicate]

Imagine a crystal lattice with discrete translational symmetry. Is there any way to obtain local periodic conserved quantities by taking a derivative (deliberately left abstract)? The discretised ...
2
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0answers
72 views

Lagrangians not related via a total time derivative lead to same Noether symmetries?

Having answered my initial two questions (v1), I now consider a third possibility. Consider two Lagrangians that both lead to equivalent equations of motion. Suppose that they are not related via a ...
3
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1answer
326 views

Many Body Physics: Hamiltonian block structure and Symmetries

Consider a many body problem of a small cluster, e.g. the 'Hubbard-Cluster' (albeit the question may be of relevance for other Hamiltonians as well): $$\mathcal{H}=\sum_{<ij>\sigma} t_{ij} ...
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102 views

Spin 1/2 wavefunction transformation under inversion and mirror symmetry

I'm considering group-theory applications to condensed matter physics now. In particular I work with the following paper: http://journals.aps.org/pr/pdf/10.1103/PhysRev.100.580 and try to understand ...
5
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3answers
660 views

How to prove a symmetric tensor is indeed a tensor?

Our professor defined a rank $(k,l)$ tensor as something that transforms like a tensor as follows: $$T^{\mu_1' \mu_2'...\mu_k'}{}_{\nu_1'\nu_2'...\nu_l'} ~=~ ...
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0answers
34 views

C, P and T for Klein-Gordon Field

Taking transformation of Klein-gordon field under C, P and T as $$\phi_{p}(t,r)= \exp(i \alpha_{p}) \phi (t,-r)\ ,$$ $$\phi_{c}(t,r)= \exp(i \alpha_{c}) \phi^\dagger (t,r)\ ,$$ $$ \phi_{T}(t,r)= ...
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1answer
78 views

Work out components $F^{01}$ and $F^{ij}$ of the antisymmetric tensor $F^{\mu\nu}$ under the Lorentz Transform [closed]

Work out explicitly how the components $F^{0i}$ and $F^{ij}$ of the antysymmetric tensor $F^{\mu\nu}$ introduced in chapter I.6 transform under a Lorentz transformation This problem is from Zee, ...
0
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2answers
351 views

When I take a Gaussian surface inside an insulating solid sphere, why does the outer volume have no effect on the electric field?

Say I try to find the magnitude of the electric field at any point within an insulating solid sphere. I know that in the case of a conductor, the electric field within it is 0. However, I have not ...
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0answers
76 views

Bondi-Metzner-Sachs (BMS) related Question(s)

I started studying the BMS group in connection with the set of papers by A. Strominger et al., also related with the supposed solution of the "Black Hole Information Paradox" by S. W. Hawking ...
6
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1answer
80 views

Is there a systematic way to obtain all conserved quantities of a system?

I'd like to know whether, given a system, there's a way to obtain all the conserved quantities. For instance if the system consists of electric and magnetic fields, the fields must satisfy Maxwell's ...
12
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1answer
197 views

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 ...
7
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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
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1answer
183 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 ...
4
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3answers
277 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 ...
12
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4answers
4k 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
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1answer
53 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 ...
0
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1answer
86 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 ...
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5answers
146 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 ...
3
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1answer
190 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 ...
9
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3answers
34k 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 ...
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0answers
65 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 ...
5
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0answers
187 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 ...
9
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5answers
536 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
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2answers
359 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 ...
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1answer
121 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
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1answer
72 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 ...
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0answers
103 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
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3answers
122 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
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50 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 ...
4
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2answers
117 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 ...
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1answer
46 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
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2answers
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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 ...
4
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0answers
80 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 ...
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1answer
661 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
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1answer
132 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 ...
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0answers
55 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!
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1answer
48 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
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4answers
1k 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
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2answers
172 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?
3
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1answer
347 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 ...
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3answers
2k 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 ...
4
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1answer
235 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 ...
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115 views

Symmetry considerations in Plane Poiseuille Flow

I'm taking a first course on fluid dynamics, and I have this (sort of) conceptual question that's been nagging me for a moment now. I can completely follow the mathematics behind the derivation of the ...
2
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1answer
122 views

Symmetry of extrinsic curvature tensor

I am trying to solve following problem: In a spacetime of signature (+, −, −, −), let $$ u^au_a = 1, \quad A_{ab} = \nabla_cu_dh^c_{\; a}h^d_{\; b}, \quad h_{ab} = g_{ab} - u_au_b $$ Show that ...