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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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}) ...
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45 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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109 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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40 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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1k 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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137 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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64 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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594 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
107 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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40 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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40 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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546 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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168 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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279 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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1k 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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215 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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97 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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1answer
102 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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20 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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96 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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69 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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178 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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158 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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43 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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3k 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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98 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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79 views

“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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246 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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4answers
114 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
106 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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2answers
132 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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138 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 ...
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156 views

Categorizing solutions to Hierarchy problem

We know that no gauge symmetry can prevent a term $m_\phi^2|\phi|^2$ for a scalar field, and that, given the quadratic loop corrections, the natural scale is $m_\phi \sim M_P$. This is related to the ...
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253 views

Relation between (super)integrability and closed orbits

Inspired by this recent question, I would like to understand from a more general and mathematical perspective why closed orbits are only found for the Kepler ($V(r) \sim 1/r$) or harmonic ($V(r) \sim ...
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41 views

Periodically connected QHO's

I've recently been thinking about what happens when you connect quantum harmonic oscillators in a periodic way. I'm actually thinking about when you take a mass-spring system (which can easily be put ...
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35 views

Occurance and disappearance of degeneneracies in a periodic structure of (quantum) LC circuits

Introductory part I'm currently studying an analytical model of coupled LC circuits, in preparation for actually performing measurements on such structures. While the final goal will struggle with a ...
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40 views

Symmetry of the Gravitational Stress Energy pseudo tensor

Recently, I have been reading on the Gravitational Stress-Energy pseudo tensor. It says in Wikipedia that one of the conditions for a suitable GSE pseudo tensor is that it has to be symmetric about ...
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1answer
98 views

Trivial conserved Noether's current with second derivatives

I'm considering a symmetry transformation on a Lagrangian $$ \delta A = \int L(q +\delta q, \dot{q} + \delta \dot{q} , \ddot{q} + \delta \ddot{q}) dt $$ the general variation takes the form $$ ...
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59 views

Noether Current and Feynman Diagrams

My question is simple. Assume that there is no anomaly and we have found from the lagrangian that there is a conserved current. I want to know what this means in terms of feynman diagrams, not in ...
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1answer
66 views

How does the Hamiltonian change when going to a moving frame?

The Hamiltonian of a free particle in a rotating frame is given by $$ H = H_0 - \omega \cdot J, $$ where $H_0$ is the Hamiltonian in the non-rotating frame, $\omega$ is the angular velocity of the ...
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1answer
82 views

systems of particles that are not symmetric or anti-symmetric; Helium 4

Suppose I have an electron and a proton, and that the electron is in the spin-up state, and that the proton is in the spin-down state. The particles are distinguishable, so I should just be able to ...
3
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1answer
788 views

Hamiltonian Noether's theorem in classical mechanics [duplicate]

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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55 views

How to prove by symmetry that tension in a section of rapidly rotating wheel act tangentially?

Suppose a thin uniform wheel of radius $r$ is rotating rapidly about its axis; its spokes have almost negligible strength. According to the book, the centripetal force is provided by the tension ...
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1answer
150 views

Does Conformal Invariance of the Polyakov Action in Conformal Gauge imply Conformal Invariance of the Pre-gauge-fixed Polyakov Action?

In bosonic string theory the Polyakov action can be put in into conformal gauge. It is then possible to show that the resulting gauge fixed action is conformally invariant. Actually it's shown that ...
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266 views

Particle hole symmetry of single site?

Let's consider I have a system with equal number of spin up and spin down particles Now I consider a single site of system,I have a state $c_{i\uparrow} ^{\dagger}\mid 0\rangle$ under particle hole ...
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144 views

Symmetry of Bloch Hamiltonian

If a crystal system preserve a symmetry C, why its Bloch Hamiltonian satisfy $H(C\vec k)=CH(\vec k)C^{-1} $
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366 views

If a symmetry operator S in a QFT annihilates the vacuum, why does S preserve the space of 1-particle states?

In the paper "Supersymmetry and Morse Theory", on the third page (p. 663 in the journal version), Witten says: "Now in any quantum field theory if a symmetry operator (an operator which commutes ...
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105 views

What are the unitary operators for various transformation?

Transformations, at least in lagrangian-symmetries context, are usualy described as uintary operators. I dont understand what are these operators exactly. For example, let's look at the Lorentz ...
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116 views

$T$-invariant Hamiltonians

If $T$ is time-reversal transformation $t\mapsto -t$, Why do $T$-invariant Bloch Hamiltonians obey $$H(-k) = T H(k) T^{-1}$$ and not $$H(k) = T H(k) T^{-1}$$ Somehow I understand the word "invariant" ...