The symmetry tag has no wiki summary.
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Topological vs. non-topological noetherian charges
What (if any) is the relationship between the conserved (non-topological) noetherian charges and topological charges? Namely, is there any "generalization" of the Noether's first theorem that includes ...
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1answer
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Diagonal matrix in k-space
I'm having some trouble with an integration I hope you guys can help me with.
I have that:
${{\mathbf{v}}_{i}}\left( \mathbf{k} \right)=\frac{\hbar {{\mathbf{k}}_{i}}}{m}$
and ...
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7answers
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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 a system, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
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3answers
410 views
Does high entropy means low symmetry?
According to Bogolubov postulate (various texts name it differently) in Non-equilibrium thermodynamics, the number of needed parameters to describe our system is decreasing with time, and finally at ...
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1answer
55 views
Gauging discrete symmetries
I read somewhere what performing an orbifolding (i.e. imposing a discrete symmetry on what would otherwise be a compactification torus) is equivalent to "gauging the discrete symmetry". Can anybody ...
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1answer
46 views
Possible states for two electrons in the helium atom
Consider the helium atom with two electrons, but ignore coupling of angular momenta, relativistic effects, etc.
The spin state of the system is a combination of the triplet states and the singlet ...
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2answers
404 views
What is the ontological status of Faddeev Popov ghosts?
We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they ...
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1answer
45 views
Baryon wave function symmetry
If a baryon wavefunction is $\Psi = \psi_{spatial} \psi_{colour} \psi_{flavour} \psi_{spin}$,
and we consider the ground state (L=0) only.
We know that the whole thing has to be antisymmetric under ...
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0answers
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A general wavefunction in a square lattice
Suppose we have a square lattice with periodic condition in both $x$ and $y$ direction with four atoms per unit cell, the configuration of the four atoms has $C_4$ symmetry. What will be a general ...
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1answer
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Gravitational field v.s. Physical variable?
I went to a talk on Newtonian mechanics some time earlier and the speaker said, and I quote,
Newton's equations of motion admit a larger symmetry group than the Galilean group alone. Therefore, ...
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19 views
Coordinate transform to exploit symmetry
I have a stochastic process that can be described the following master-equation:
$$
\partial_{t}P(x,y)=-\left(W_{12}(x,y)+W_{13}(x,y)+W_{21}(x,y)+W_{23}(x,y)+W_{31}(x,y)+W_{32}(x,y)\right)P(x,y)\\
...
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Question about Noether theorem
For the Noether theorem for pseudoeuclidean 4-spacetime a-current $J_{a}^{\mu}$ is equal to
$$
J_{a}^{\mu} = \frac{\partial L}{\partial (\partial_{\mu}\Psi_{k})}Y_{k, a} - \left( \frac{\partial ...
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1answer
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“WLOG” re Schwarzschild geodesics
Why, when studying geodesics in the Schwarzschild metric, one can WLOG set
$$\theta=\frac{\pi}{2}$$
to be equatorial? I assume it is so because when digging around the internet, most references seem ...
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0answers
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How to define the mirror symmetry operator for Kane-Mele model?
Let us take the famous Kane-Mele(KM) model(http://prl.aps.org/abstract/PRL/v95/i22/e226801 and http://prl.aps.org/abstract/PRL/v95/i14/e146802) as our starting point.
Due to the time-reversal(TR), ...
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1answer
424 views
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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1answer
197 views
Coulomb gauge fixing and “normalizability”
The Setup
Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as
$$
A_\mu\to ...
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1answer
249 views
A simple model that exhibits emergent symmetry?
In a previous question Emergent symmetries I asked, Prof.Luboš Motl said that emergent symmetries are never exact. But I wonder whether the following example is an counterexample that has exact ...
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2answers
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A question on the existence of Dirac points in graphene?
As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2$\times$2 Hermitian matrix $H(k_x,k_y)$ has two degenerate points $K$ ...
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Curie's principle in electromagnetic field theory
I am looking for some explanation and if possible also some references about the applications of Curie's principle in electromagnetic field Theory, precisely in the computation of magnetic (resp. ...
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0answers
35 views
Spherical charge in two different dielectric materials
I am trying to freshen up my memory about electrical fields and I came across this exercise from school.
A sphere with a constantly distributed charge is located in between two different dielectrics ...
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0answers
187 views
Extended Born relativity, Nambu 3-form and ternary (n-ary) symmetry
Background: Classical Mechanics is based on the Poincare-Cartan two-form
$$\omega_2=dx\wedge dp$$
where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. By the other hand, ...
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1answer
250 views
Why does a transformation to a rotating reference frame NOT break temporal scale invariance?
Naively, I thought that transforming a scale invariant equation (such as the Navier-Stokes equations for example) to a rotating reference frame (for example the rotating earth) would break the ...
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4answers
354 views
When can a global symmetry be gauged?
Take a classical field theory described by a local Lagrangian depending on a set of fields and their derivatives. Suppose that the action possesses some global symmetry. What conditions have to be ...
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1answer
582 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 point-views:
Anomalies are due to the fact that quantum field ...
2
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1answer
61 views
Invariance, covariance and symmetry
Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? ...
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1answer
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Schrödinger Equation
I am reading up on the Schrödinger equation and I quote
Because the potential is symmetric under $x\to-x$, we expect that there will be solutions of definite parity.
Could someone kindly explain ...
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0answers
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What is kappa symmetry?
On page 180 David McMohan explains that to obtain a (spacetime) supersymmetric action for a GS superstring one has to add to the bosonic part
$$
S_B = -\frac{1}{2\pi}\int d^2 \sigma ...
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2answers
349 views
Lorentz invariance of the 3 + 1 decomposition of spacetime
Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example
$$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$
($N$ is called lapse, $N_a$ is ...
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2answers
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Eigenfunctions in periodic potential
For Hamiltonian $\operatorname H$ and lattice translation operator $\operatorname T$, if
$$\operatorname H\psi=E\psi, \qquad \operatorname T\psi=e^{ik\cdot R}\psi,$$
and
$$\operatorname ...
3
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2answers
92 views
What is a symmetry of a physical system?
If I understand correctly, in many context in physics (quantum mechanics?), a physical system is specified by giving its Hamiltonian. I also hear that symmetries are rather essential.
As far as the ...
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0answers
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CP-symmetry and Ward identities and finite temperature
I have a few questions about Ward-identities which I summarize here. For each I am very greateful for answers and references to literature.
Wikipedia states about Ward-identities:
The ...
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1answer
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A simple example of symmetry setting the properties of a Physical System
Does anybody know of an example were one could derive some important properties of a physical system from a symmetry of said system.
I´m specially looking for simple classical examples, which could ...
3
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1answer
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What are the conserved charges related to the Virasoro generators?
I have just learned from reconsidering my demystified book, that when conformally maping the worldsheet of a closed string to the complex plain by using the transformation $z = e^{\tau + i\sigma}$ ...
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1answer
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Why do we classify states under covering groups instead of the group itself?
Why do we always classify states under covering group representations instead of the group itself? For example see the following picture I lifted from 'Symmetry in physics' by Gross
So in the first ...
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1answer
96 views
Lorentz invariance of the wave equation
I want to show that the 2-d wave equation is invariant under a boost, so, the starting point is the wave equation
$$\frac{\partial^2\phi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2\phi}{\partial ...
4
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1answer
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What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT?
What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT? The question is motivated by this preprint arXiv:1203.0609 by Murayama and Watanabe.
Also, what ...
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4answers
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What is the usefulness of the Wigner-Eckart theorem?
I am doing some self-study in between undergrad and grad school and I came across the beastly Wigner-Eckart theorem in Sakurai's Modern Quantum Mechanics. I was wondering if someone could tell me why ...
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1answer
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Energy-momentum conservation without translation symmetry?
As I checked, the energy-momentum tensor defined as ${T^\mu}_\nu=\frac{\partial {\cal L}}{\partial(\partial_\mu \phi)}\partial_\nu \phi-{\cal L}{\delta^\mu}_\nu$ at the solution $\phi$ of equation of ...
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3answers
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Noether's current expression in Peskin and Schroeder
In the second chapter of Peskin and Schroeder, An Introduction to Quantum Field Theory, it is said that the action is invariant if the Lagrangian density changes by a four-divergence.
But if we ...
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2answers
268 views
Galilean invariance of the Schrodinger equation
I am only asking this question so that I can write an answer myself with the content found here:
http://en.wikipedia.org/wiki/User:Likebox/Schrodinger#Galilean_invariance
and here:
...
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3answers
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Maxwell equations invariant under Lorentz transformation but not Galilean transformations
Why Maxwell equations are not invariant under Galilean transformations, but invariant under Lorentz transformations? What is the deep physical meaning behind it?
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5answers
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Form of the Classical EM Lagrangian
So I know that for an electromagnetic field in a vacuum the Lagrangian is $\mathcal L=-\frac 1 4 F^{\mu\nu} F_{\mu\nu}$, the standard model tells me this. What I want to know is if there is an ...
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3answers
373 views
Must all symmetries have consequences?
Must all symmetries have consequences?
We know that transnational invariance, for example, leads to momentum conservation, etc, cf. Noether's Theorem.
Is it possible for a theory or a model to have ...
4
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2answers
112 views
Crystal Angular Momentum
In a crystal, we don't have full translational symmetry, but we still have discrete translations. This allows us to define "crystal momentum" that is conserved modulo a reciprocal lattice vector.
In ...
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2answers
234 views
Why and how does symmetry work in circuits?
Why symmetry work in circuits? In my book there is no mention explanation as such for symmetry arguments and circuits. But there are circuits that are very difficult to solve without symmetry. Also I ...
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2answers
135 views
Does a constant factor matter in the definition of the Noether current?
This is a very basic Lagrangian Field Theory question, it is about a definition convention. It takes much more time to typeset it than answering, but here it is:
Consider a field Lagrangian with only ...
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2answers
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What symmetries does a lattice calculation need to preserve?
I've heard that it is impossible to have a properly Lorentz-invariant lattice QFT simulation, as the Lorentz invariance is spoiled by the nonzero lattice distance $a$. I've also heard that there are ...
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1answer
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Spontaneous breaking of Lorentz invariance in gauge theories
I was browsing through the hep-th arXiv and came across this article:
Spontaneous Lorentz Violation in Gauge Theories. A. P. Balachandran, S. Vaidya. arXiv:1302.3406 [hep-th]. (Submitted on 14 ...
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1answer
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How do we make symmetry assumptions rigorous?
I have, for instance, a problem with a spherically symmetric charge distribution. I deduce here, in order to solve the problem easily, that the corresponding electric field must be symmetric. How is ...
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Dimensional transmutation in Gross-Neveu vs others
Firstly I don't know how generic is dimensional transmutation and if it has any general model independent definition.
Is dimensional transmutation in Gross-Neveau somehow fundamentally different ...
