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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140 views

Behavior of the Electric- and Magnetic-field under time reversal and parity

The behavior of the electric- $\mathbf{E}$ and the magnetic-field $\mathbf{B}$ und time reversal and parity can be calculated in different ways. My first solution is to study the transformation ...
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2answers
172 views

Conservation of energy and Killing-field

In general relativity we have no general conservation of energy and momentum. But if there exists a Killing-field we can show that this leads to a symmetry in spacetime and so to a conserved quantity. ...
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445 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. ...
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52 views

Combinatorics of fourth order feynman diagram

I am trying to calculate how many different forth order feynman loop diagrams I can produce. I know that for 2nd order it is 6x3x2 thus 3! since you start with 3 lines coming out of each vertex so 6 ...
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2answers
193 views

Is there something more to Noether's theorem?

From the definition of Lagrangian mechanics, Noether's theorem shows that conservation of momentum and energy comes from invariance vs time and space. Is the reverse true? Are Lagrangian mechanics ...
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1answer
392 views

Invariance of action $\Rightarrow$ covariance of field equations?

Invariance of action $\Rightarrow$ covariance of field equations? Is this statement true? I have only seen examples of this, like the invariance of Electromagnetic action under Lorentz ...
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48 views

Anisotropy Axis

I am trying to identify the anisotropy axis of a patterned two-dimensional surface, such as one with parallel sets of stripes...is the anisotropy axis parallel or perpendicular to the stripes? ...
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31 views

What are gyrotropic crystals?

I am reading a paper about spin photocurrents that talks about gyrotropic crystals, but I do not find any good explanation what gyrotropy is or how to find out whether a crystal belongs to the ...
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0answers
79 views

Non-symmetry of a lagrangian

If a transformation $\Phi \rightarrow \Phi + \alpha \partial \Phi/ \partial \alpha$ is not a symmetry of the Lagrangian, then the Noether current is no longer conserved, but rather ...
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0answers
99 views

Constructing Killing tensors from Killing vectors

Background: After reading about Carter constant and symmetries in GR, I became interested in Killing tensors. I tried reading this paper by Alan Barnes, Brian Edgar and Raffaele Rani, discussing ...
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3answers
403 views

Why is Planck's constant the same for all particles?

This question came to me while reading Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from? This question has a nice answer that explains that wave number has be ...
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1answer
1k views

Do an action and its Euler-Lagrange equations have the same symmetries?

Assume a certain action $S$ with certain symmetries, from which according to the Lagrangian formalism, the equations of motion (EOM) of the system are the corresponding Euler-Lagrange equations. Can ...
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1answer
87 views

Gravitational force and potential in infite slab

Let's say that we have an infinite slab of height $2h$ and mass density $\rho$. Let's define $x,y$ as the axis parallel to the slab and $z$ as the perpendicular one, with $z=0$ at the middle of the ...
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429 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 ...
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5answers
1k views

Noether Theorem and Energy conservation in classical mechanics

I have a problem deriving the conservation of energy from time translation invariance. The invariance of the Lagrangian under infinitesimal time displacements $t \rightarrow t' = t + \epsilon$ can be ...
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2answers
456 views

Killing Vectors in Schwarzschild Metric

Given the Schwarzschild metric with $(-,+,+,+)$ signature, $$ds^2=-\left(1-\frac{2M}{r}\right)dt^2+\left(1-\frac{2M}{r}\right)^{-1}+r^2(d\theta^2+\sin^2\theta\,d\phi^2)$$ the lack of dependence of ...
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1answer
67 views

Transformations of states in quantum mechanics

In Classical Mechanics we usually describe the possible configurations of a system by points on a smooth manifold $M$ which is the configuration manifold of the system. In that case, when we talk ...
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3answers
62 views

Examples of non-linear field symmetries?

Consider a Lagrangian theory of fields $\phi^a(x)$. Sometime such a theory posseses a symmetry (let's talk about internal symmetries for simplicity), which means that the Lagrangian is invariant under ...
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2answers
174 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 ...
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1answer
123 views

How to find symmetry transformations?

For a given Lagrangian $$ {\cal L} = - \frac{1}{4} F_{\mu \nu} F^{\mu\nu} + |D_{\mu} \phi|^2 -V (\phi) $$ with $\phi = \frac{1}{\sqrt{2}} (\phi^1 + i \phi^2)$, there are the infinitesimal local ...
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36 views

Advanced Quantum Mechanics (Galilean transformations)

I have been reading quantum mechanics textbook by Ballentine, and in the third chapter, he says that the eigenvalues of the transformed operator, A', must remain same as those of A. I am confused ...
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1answer
42 views

Isotropic of Inertial frame?

My understanding of isotropic is the a particular physics law remain same no matter at what direction I look at it? Now suppose in case of inertial frame, we know that its is homogeneous and ...
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1answer
56 views

Lagrangian is isotropic in space

In Landau & Lifshitz Mechanics, while deriving the properties of Lagrangian of a free particle in inertial frame, he uses the following points $:$ As space is homogeneous in inertial frame, a ...
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20 views

Symmetry of retarded R-current correlator in $\mathcal{N}=4$ Super Yang-Mills

The retarded correlator of the R-current $J_\mu$ of $\mathcal{N}=4$ Super Yang-Mills theory is $$ C_{\mu\nu}(x-y)=-i\theta(x^0-y^0)\langle[J_\mu(x),J_\nu(y)]\rangle. $$ In this paper in eq. (2.4), I ...
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1answer
2k 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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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 ...
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26 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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5answers
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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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1answer
55 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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4answers
531 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 ...
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10answers
5k views

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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3answers
1k views

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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34 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. ...
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4answers
192 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
35 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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1answer
97 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
91 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 ...
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0answers
68 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 ...
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1answer
315 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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97 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 ...
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3answers
613 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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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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76 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, ...
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2answers
302 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
71 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 ...
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1answer
79 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
2k views

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
195 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
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 ...