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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Emergent symmetries

As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
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Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are?

Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are? Coleman-Mandula is often cited as being the key theorem that leads us to consider Supersymmetry for ...
16
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322 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 ...
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24 views

Symmetries, source terms, boundary conditions

If I recall correct you can say that e.g. the electric vectorfield is only a function of the radius if the source terms (charge) is spherical and uniform so that a group action that rotates space ...
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Is the converse of Noether's first theorem true: Every conservation law has a symmetry?

Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is the converse true: Any conservation law of a physical ...
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52 views

Strong interaction under $SO(3)$ isospin transformation

I'm given the following strong interaction: $$S = \int d^{4}x [\frac{1}{2} \partial_{\mu} \phi^{a} \partial^{\mu} \phi^{a} - \frac{m^2}{2} \phi^{a} \phi^{a}] ,\qquad a = 1,2,3 \text{.}$$ It is stated ...
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383 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 ...
49
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10answers
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Is there something similar to Noether's theorem for discrete symmetries?

Noether's theorem states that, for every continuous symmetry of an action, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
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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?
0
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1answer
30 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
143 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 ...
0
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1answer
34 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 ...
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94 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 ...
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1answer
82 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 ...
0
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0answers
17 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
65 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
281 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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79 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
402 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
32 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)= ...
1
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1answer
63 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
126 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
62 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 ...
4
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1answer
54 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 ...
8
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2answers
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Deriving Birkhoff's Theorem

I am trying to derive Birkhoff's theorem in GR as an exercise: a spherically symmetric gravitational field is static in the vacuum area. I managed to prove that $g_{00}$ is independent of t in the ...
12
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1answer
180 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 ...
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3answers
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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
118 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
223 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
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 ...
5
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2answers
90 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
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3answers
426 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 ...
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1answer
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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 ...
37
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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
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1answer
80 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 ...
5
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2answers
64 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 ...
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100 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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120 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 ...
8
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24k 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
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0answers
43 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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179 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
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108 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 ...
9
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477 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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1answer
88 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
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2answers
343 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 ...
4
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0answers
775 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?
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1answer
96 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 ...
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1answer
63 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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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 $n$ ...
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115 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}) ...