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 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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51 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 $n$ ...
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70 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}) ...
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35 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 ...
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94 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 ...
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70 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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30 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 ...
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937 views

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 ...
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50 views

Hermitian conjugate of an antiunitary transformation

In quantum mechanics, one often considers symmetry transformations which are defined in terms of operators which do not change the norm of states in the Hilbert space. For the Wigner's theorem, this ...
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35 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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465 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 ...
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1answer
58 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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114 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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96 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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1answer
139 views

Point group symmetries and unit cell

I was wondering if the unit cell (of a given lattice) had to have every point group symmetries of the lattice it defines ? I guess there is no unique way to define a unit cell and that it may not have ...
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344 views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
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36 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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11 views

How do you reduce a monkhorst pack mesh onto the irreducible brillouin zone using crystal symmetry operations?

How do you reduce a Monkhorst-Pack mesh onto the irreducible Brillouin zone using crystal symmetry operations? How can the star of a reciprocal space point be determined? A reference and/or an ...
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30 views

How is the irreducible Brillouin zone for an arbitrary crystal structure determined?

If one knows the atomic positions and the lattice basis vectors, as is required for any density functional theory calculation input, how can the irreducible Brillouin zone be determined? Thanks!
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28 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, ...
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4answers
64 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 ...
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2answers
153 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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1answer
201 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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115 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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793 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 ...
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169 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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55 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 ...
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75 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 ...
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124 views

Symmetries of the action of the free classical Klein-Gordon field

I've read that the action for the free classical Klein-Gordon field $$S = \int \mathrm{d}^4x~ \mathcal{L} = \frac{1}{2} \int \mathrm{d}x^4 \left(\partial_\mu \phi(x) \, \partial^\mu \phi(x) - ...
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18 views

How to experimentally identify the exposed face of a crystal?

After depositing a material (e.g, TiO2) on a substrate, what methods can I use to check whether the material is crystalline, and what face (e.g, 001, 101, etc..) of the crystal is exposed?
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83 views

Path of light as it travels between two black holes

What would happen to light passing through a narrow space between the event horizons of two equal-mass black holes? Would it deviate or follow a straight path?
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83 views

Degenaracy in mass of $8$ and $27$ reps of $SU(3)$ in Coleman's Aspects of Symmetry [closed]

In Coleman's Aspect of symmetry he proposes an amusing problem in the first chapter. It asks us to consider a set of eight pseudo-scalar fields transforming in the adjoint representation of $SU(3)$. ...
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253 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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31 views

Symmetry axis and products of inertia

So if we have an object that has a symmetry axis let us say $z$-axis is a symmetry axis does this mean that the product of inertia $I_{zx} = I_{zy} = 0$? And if that is true why is it true ...
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141 views

In QFT how do you write down the most general interactions?

This past year I took a QFT class and I now feel comfortable solving scattering problems, but I am still a bit perplexed by how physicists write down a Lagrangian in the first place. In particular, ...
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4answers
349 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 ...
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1answer
70 views

Does isotropy imply homogeneity?

This question comes from exercise 27.1 in Gravitation by Misner, Thorne and Wheeler. They required the following: Use elementary thought experiments to show that isotropy of the universe implies ...
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5answers
310 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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38 views

A question about a consequence of symmetry in $\phi^4$ theory

Why does the symmetry $\phi→-\phi$ mean that an amplitude can be written as $\alpha+\beta p^2+\gamma p^4+...$ without the odd terms in $p$? I understand that, due to this symmetry, any diagram in ...
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2k views

Symmetric potential and the commutator of parity and Hamiltonian

In one dimension - How can one prove that the Hamiltonian and the parity operator commute in the case where the potential is symmetric (an even function)? i.e. that $[H, P] = 0$ for $V(x)=V(-x)$
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Only get part of commutator form expanding to third order in generator expression

(Shankar 12.2.4) Let $U[R(\epsilon_z\hat k)] = I - {i\over\hbar}\epsilon_z L_z$ be the infinitesimal generator for rotation operators, and $T(\vec\epsilon) = I - {i\over\hbar}\vec\epsilon\cdot\vec ...
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41 views

Conserved quantity corresponding to reflection symmetry

I know about Noether's theorem, but I don't actually know how to use it myself. Suppose our universe were symmetric with respect to reflections about planes. What conserved quantity would then exist ...
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Is hidden symmetry the same concept as 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 ...
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“Rotating any system of charges causes a corresponding rotation of the electric field.”- What is the proof?

While I was reading 'symmetry' from wikipedia, then I came to this statement: ...For example, an electric field due to a wire is said to exhibit cylindrical symmetry, because the electric field ...
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2answers
213 views

What is meant by “unique direction” in most of the arguments in application of Gauss' Law?

This term is really bothering me a lot. While explaining the radial direction of electric field of a uniformly charged sphere, my book writes: Notice the use of argument of symmetry. There is no ...
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1answer
908 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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94 views

Energy conservation without action principle?

The normal tagline for energy conservation is that it's a conserved quantity associated to time-translation invariance. I understand how this works for theories coming from a Lagrangian, and that this ...
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1answer
55 views

What are the symmetry criteria for continuous phase transitions in Landau theory?

My understanding is that within Landau theory, a continuous phase transition is only possible if certain symmetry rules are satisfied. (These rules represent necessary but not sufficient conditions ...
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96 views

Derivation of law of inertia from Lagrangian method (Landau)

I'm reading Landau's Book. He tries to conclude the law of inertia from the Lagrange equations. For that, he argues (by nice suppositions about space and time), that the lagrangian must depend only ...
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96 views

How is the Full Standard Model group representation displayed?

I have often seen, on YouTube lectures and textbooks, the direct product gauge group representation listed below and it is often accompanied with a statement to the effect that "this is how we sum ...