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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What is the symmetry of the Penrose tiling? [migrated]

What is the symmetry of the Penrose tiling? Simply C5 or bigger? Any simple proof that the tiling is a complete cover of the plane?
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43 views

What's the corresponding symmetry of enstrophy conservation?

In fluid mechanics, especially 2D turbulence study, people talk about conservation of enstrophy. But I can't really understand enstrophy very well, and what's the corresponding symmetry of enstrophy ...
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57 views

I want to decompose a tensor product using Littlewood-Richardson rule, How do I find the component of this in each irreducible space?

Let me set up the notation I am using. $(abc,de)$ denotes the standard Young tableau where the first row is $abc$ and the second row is $de$. Each young tableau corresponds to the young symmetriser, ...
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104 views

Why is the inertia ellipsoid of a higher symmetry than the rigid body?

I was always puzzled by this fact. A uniform cube has a sphere-shaped inertia ellipsoid. The sphere has a higher symmetry then the cube. Is there any deep reason or implication behind it?
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70 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?
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34 views

Argument for symmetry of potential of a spherical capacitor filled with dielectric

A spherical capacitor with inner radius $r_1$ and outer radius $r_2$ is filled with dielectric material with permittivity $\epsilon=\epsilon_0+\epsilon_1\cos^2\theta $. $\theta$ is the polar angle. ...
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146 views

Noether's Theorem: Foundations

I'm wondering on what principles Noether's theorem foots. More precisely: The action is a functional on the fields only. Why do we consider then variations of the space time too? In principle careful ...
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72 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
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2answers
55 views

Gravitational force due to asymmetric Earth shell

http://en.wikipedia.org/wiki/Shell_theorem According to above link the gravitational force inside a symmetrical shell due to itself is zero. Is it also true for an asymmetrical shell?
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66 views

Is there a physical interpretation to invariant random matrix ensembles?

Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
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44 views

Pions as a superposition of quark states

in Isospin space there are two fundamental states called up and down quarks, which satisfy the following eigenvalue equations: $I u = (1/2) u$, $I d = (1/2) d$ and $I_3 u = (1/2) u, I_3 d = (-1/2) ...
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1answer
98 views

Conceptual question about field transformation

(c.f Conformal Field Theory by Di Francesco et al, p39) From another source, I understand the mathematical derivation that leads to eqn (2.126) in Di Francesco et al, however conceptually I do not ...
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51 views

Local symmetry and General Relativity

First I want to consider an example of 1D motion. Lagrange equation: $$ \frac{d}{dt} \frac{\partial L}{\partial \dot x} - \frac{\partial L}{\partial x} = 0 $$ If we transform $ L \rightarrow L+a $ ...
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1answer
60 views

Reversing Noether's theorem [duplicate]

Noether's theorem states: any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is this statement invertible? I mean, if a conservation law exists, this ...
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54 views

Why is the $SO(4)$ symmetry of the Hydrogen atom called dynamical?

Why dynamical? My previous quantum mechanics teacher could not answer it.
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18 views

Association of financial phenomena/indications with the conservation laws of Black Scholes equation

For a while I've been doing research on methods of obtaining conservation laws via the symmetries of differential equations (DEs). I'm presently doing research on identifying financial ...
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5answers
517 views

Why is the electric field of an infinite insulated plane of charge perpendicular to the plane?

I'm studying Gauss' Law, and I came across a section where we're supposed to find the electric field of various shapes (like an infinite line of charges, etc), and for an infinite plane with a uniform ...
5
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1answer
88 views

Kac-Moody algebras in 5 dimensional Kaluza-Klein theory

I am trying to make sense to the issue of how does the Kac-Moody algebra encode the symmetries of the non-truncated theory. Let's contextualize a little bit. Ok, so in the 5 dimensional Kaluza-Klein ...
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2answers
41 views

Charge inside a sphere

Suppose I have a sphere of radius $r$ with all the charge residing on the surface, distributed uniformly i.e. charge density $\sigma$ is constant. I want to find the electric field created by this ...
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72 views

A Subtle Connection Between Time Dilation in SR and GR - Why is this so?

I've been reading a book on General Relativity lately (Gravitation and Cosmology, Weinberg), and I was reading about the weak field approximation. It derived the time dilation in a weak gravitational ...
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2answers
58 views

Gauss's Law for a Uniformly Charged Solid Sphere [duplicate]

We want to calculate $\vec{E}$ at a distance $r$ from the center $O$ of a spherical polar coordinate system. Let the point on the Gaussian surface at which we want to calculate $\vec{E}$ is ...
2
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1answer
89 views

Are diffeomorphisms a proper subgroup of conformal transformations?

The title sums it pretty much. Are all diffeomorphism transformations also conformal transformations? If the answer is that they are not, what are called the set of diffeomorphisms that are not ...
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13 views

Computing Parity by numerical tables of characters

I have a table of the characters of a set of wavefunctions for different points in reciprocal space and for different band indices (this is for a solid). For the case of a single irreducible ...
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37 views

Quick question on degeneracy of harmonic oscillator states

I'm currently learning about symmetry between particles. For a simple case of two non-interacting particles at $x_1$ and $x_2$, we know that the wavefunction can be written as $\psi_{n_1, n_2} = ...
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72 views

Why is the projective symmetry group (PSG) called projective?

As discussed by Prof.Wen in the context of the quantum orders of spin liquids, PSG is defined as all the transformations that leave the mean-field ansatz invariant, IGG is the so-called invariant ...
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76 views

Euclidean functional Integrals

In the chapter "Uses of Instantons" from the book "aspects of symmetry" by Sidney Coleman I have come across the euclidean version of the path integral in semi-classical approximation. To evaluate the ...
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77 views

Possible mechanics based on the known symmetries in the nature (investigating rumor)

Somewhere I've heard about a relative new mathematical result regarding mechanics. Specifically, there is a list of the known symmetries of mechanics (both Newtonian and relativistic), i.e. different ...
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42 views

What is the minimal symmetry required for a spin Hamiltonian to describe a spin-liquid ground state?

Let's restrict to the case of spin-1/2 system. As we know, a spin-liquid (SL) state is the ground state of a lattice spin Hamiltonian with no spontaneous broken symmetries (sometime it may ...
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2answers
70 views

Symmetry arguments in solving problems

There was a question which involved calculation of final charges on two spheres when one uncharged and the other having charge $Q$ were brought in contact with each other. (radius same). If potential ...
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1answer
73 views

Translations and Noether's Theorem

I'm fine with $U(1)$ symmetry and Noether's Theorem, but struggling with the translations of the field; namely $$\phi'(x^{\mu})=\phi(x^{\mu}-a^{\mu}),$$ where $a^{\mu}$ constant four-vector ...
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52 views

Symmetry factor of tree diagram

In Mark Srednicki's Quantum field theory(page 89) it says This is a general result for tree diagrams (those with no closed loops): once the sources have been stripped off and the endpoints ...
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23 views

How to easily calculate lengths (or relative lengths) of paths between symmetry points in BZ

I am trying to easily calculate the length between special kpoints within the BZ of the 32 point groups in a crystal system. I am calculating the lengths in order to scale k point sampling along these ...
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1answer
95 views

Plotting a bandstructure along High-symmetry points when kx,ky,kz is known

Suppose you know kx,ky,kz points along with the corresponding energies. Basically, you know about the 4-D E(k) dispersion. How you do then convert that data into the bandstructure plots you commonly ...
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1answer
28 views

Behavior of Pion-Mediated Nuclear Force before Electroweak Symmetry Breaking?

When Chiral Symmetry was exact, as it was before EWSB due to the lack of mass terms for quarks, would the residual strong force have infinite range? Related to this, does the Negative Beta Function ...
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144 views

Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
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1answer
48 views

Spatial part of wavefunction of helium, both electrons are in ground state

If both electrons are in ground state, characterized by $(1s)^2$, this means that n =1, l = 0. The two electrons occupy the same energy and space (why doesn't pauli exclusion principle prevent this?), ...
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172 views

A question about Feynman diagram and symmetry factor

Consider a $\varphi^3$ theory: $$ Z_1(J) \propto \exp\left[\frac{i}{6} Z_g g\int \mathrm{d}^4 x \left(\frac{1}{i}\frac{\delta}{\delta J}\right)^3\right] Z_0(J), $$ where $$ Z_0(J) = ...
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1answer
47 views

Unit determinant for relevant symmetry groups in QFT

When treating QFT we want our theory to be invariant under different symmetry groups, for example, the Standard Model is a non-abelian gauge theory with the symmetry group $U(1)×SU(2)×SU(3)$. ...
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68 views

Intuition Behind Conservation of Angular Momentum

I'm having a fairly hard time understanding the intuition behind Noether's derivation of the conservation of angular momentum from the rotational invariance of the Lagrangian, though I do understand ...
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186 views

What are particle multiplets in the Standard Model?

The particles of the standard model are often displayed in groupings known as multiplets. I know that this somehow relates to the underlying symmetries of the standard model, which can be viewed as ...
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78 views

Why do the states of a spin multiplet have to have the same symmetry?

This was said in Prof. Balakrishnan lecture 19 on quantum mechanics for the case of exchange symmetry, but he showed no reason why. For example, the system corresponding to two spin $\frac{1}{2}$ ...
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54 views

Galilean Transform

I tried to solve a problem using two different ways and I had some trouble, the problem is: We define a symmetry transform of the expected value of $\vec{P}$ like this: $$\langle \psi|\vec{P}|\psi ...
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2answers
101 views

Lorentz invariance?

What exactly is meant by Lorentz invariance? Is it just an experimental observation, or is there a theory that postulates it? What quantities do we expect to be Lorentz invariant? Charge? Charge ...
6
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1answer
393 views

Easy proof of Noether's theorem? [duplicate]

Where could I find an easy proof of Noether's theorem? I mean I know that the variation must be $ 0=\delta S = (EULER-LAGRANGE)+ (CONSERVED\, \, \, CURRENT) $ for the case of a particle $q(t)$. I ...
3
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1answer
139 views

Interpretation of Conjugate Momentum in Field Theory

The conjugate momentum density, following as a conserved quantity with Noethers Theorem, from invariance under displacement of the field itself, i.e. $\Phi \rightarrow \Phi'=\Phi + \epsilon$, is given ...
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61 views

Questions on degenerate ground states and the thermodynamic limit?

For example, let's consider a $N$ spin-1/2 system on a lattice described by the Hamiltonian $H$. My questions are: (1) If $H$ has either global $SU(2)$ spin-rotation symmetry or time-reversal ...
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98 views

Examples of symmetric field collapse to produce asymmetry

It would really help me with an idea I have if I could see how something such as a symmetric field could collapse to something asymmetric. I know that if $x$ occures before $y$ is symmetric, then $y$ ...
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93 views

Forces, symmetry, and asymmetry

The concept of symmetry is one of the most promising and misunderstood concepts in physics. If one consider Hermann Weyl ("Symmetry"; ISBN-13: 978-0691023748), "As far as I see, all a priori ...
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what kind of system respects $SU(N)$ symmetry?

I read this post, Is the symmetry group of two spin 1/2 particles $SU(2) \times SU(2)$ or $SU(4)$? If the picked answer is correct, can I believe that an $N$-degenerate system respects $SU(N)$ ...
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90 views

Solving the Schrodinger equation with appropriate symmetry

In the paper Markov Fields by Edward Nelson the introduction section claims that analytically continuing a Markov process with appropriate symmetry properties yields the solution of the Schrodinger ...