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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Isolated system and mutual interaction potential

We know that the total linear momentum of a closed (isolated) system is conserved due to homogeneity of space (Landau and Liftshitz, page 15, Mechanics). Hence for an isolated system of two bodies ...
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85 views

Why are there only two linearly independet quartic Higgs terms for the adjoint $24$ in $SU(5)$ GUTs?

I've read the statement in countless papers, for example, here Eq. 4.2 or here Eq. 2.1 without any further explanation or reference, that the "most general renormalizable Higgs potential" for an ...
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2answers
73 views

Is there a proof that space expanding produces observers at all points that see what we see?

I know that galaxies are moving away from us, and so can see that it's intuitive that if space was expanding, then the astronomical observations from Earth would be the same as at all other points in ...
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1answer
41 views

Is it necessary to prove the existence of an operator representing symmetry on Hilbert space?

Is there any need to prove the existence of an operator $U$ which represents the action of symmetry transformation on rays in Hilbert space? Or is it enough just to prove that it is unitary and linear ...
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34 views

Symmetry Arguments: Flow Through Cylinder

Why can for symmetry reasons a steady, viscous, incompressible flow, obaying the N.S equation: $$\rho(v \nabla)v = -\nabla p + \eta \Delta v $$ That flows through a cylindrical(very long) pipe not ...
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46 views

Why are symmetrical structures highly stable?

What makes symmetrical structures(geometry) highly stable? It is perfect to say that the forces acting on a symmetrical structure is balanced and hence stable. But why is it so? To be more specific, ...
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141 views

Casimir Invariants of the Galilean group

I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I ...
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23 views

$SU(2)$ symmetry and conservation law in condensed matter systems [closed]

My question has a few parts, I know from Noether that if there is a symmetry in a Hamiltonian, there is a conservation law. What would be the conservation law associated with $SU(2)$ symmetry? ...
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237 views

Why does Weyl invariance imply a traceless energy-momentum tensor?

I've begun to self-study String Theory from Polchinski and Becker, Becker and Schwarz. I don't see why the fact that the Polyakov action is invariant under Weyl transformations is related to the ...
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2answers
446 views

Time reversal and parity symmetry

I was previously under the misapprehension that time $T$ and parity $P$ symmetries in conjunction ($PT$) were a reflection in $(3+1)$-dimensional space-time, where $$P: \vec x \to -\vec x$$ $$T: t ...
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1k views

What is the role of the vacuum expectation value in symmetry breaking and the generation of mass?

Consider a theory of one complex scalar field with the following Lagrangian. $$ \mathcal{L}=\partial _\mu \phi ^*\partial ^\mu \phi +\mu ^2\phi ^*\phi -\frac{\lambda}{2}(\phi ^*\phi )^2. $$ The ...
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2answers
130 views

Does the conservation of the Wronskian follow from Noether's principle?

Noether's principle is the paradigm that symmetries of Hamiltonian and Lagrangian systems correspond to conservation laws of various kinds. Consider a one-dimensional harmonic oscillator $$\tag{*} ...
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85 views

Deeper principles in classical mechanics

While teaching introductory physics, my professor explained that the conservation of linear momentum, conservation of energy and conservation of angular momentum are based on deeper principles in ...
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46 views

Coleman Mandula theorem and translations

I don't know what Coleman Mandula theorem is, however if I were forced to say something about it, I will say it is a statement that suggests that internal and spatial symmetries have no unique ...
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1answer
140 views

Why does Wikipedia equate hidden symmetry with 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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57 views

Derivations of Newton's laws?

I feel convinced that the mathematics behind newtons laws can be derived from Noether's symmetry theorems. The fact that displacement s can be described by a cartesian coordinate system with a ...
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24 views

Understanding what a tranformation on a Ray and Hilbert space

I've been referring to Chapter 2 of Introduction to Quantum Field Theory by Weinberg where he talks about symmetries and how they go about. Now, there are two points that he mentions. A ray, which by ...
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1answer
102 views

Is the cosmological time grosso modo isochrone?

Is the cosmological time grosso modo isochrone? by analogy with space isotropy. Or else do we have possibly great differences by analogy with great voids in the space. We know that it's not strictly ...
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71 views

Part of a Wigner theorem [closed]

I was trying to understand why there should exist operator in Hilbert space to correspond to any symmetry transformation and found about Wigner's theorem. In it, I can see that any transformed vector ...
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3answers
98 views

Thinking about the properties of 'nothing' [closed]

If a certain identifiable part of space that has no type of measurable energy fields manifesting 'in it' for a given duration ; is such a totally empty space the same as 'nothing'? Anything with any ...
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1answer
36 views

Existence of representation of symmetry transformation

There is a simple fact that we can change our point of view and that physical laws should remain the same, id est, outcomes of our experiments should be the same no matter from which frame of ...
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1answer
218 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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39 views

Symmetries of a Lagrangian density

Given some Lagrangian density as this how in general can one finds it's symmetries that give conserved currents? For example in this case U(1) is ok, but are there others? Do you know some book ...
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167 views

Spontaneous symmetry breaking to subspace not giving massless bosons

I'm currently trying to understand spontaneously symmetries broken in general and have stumbled upon a weird result which doesn't seem to correspond to my knowledge about broken gauge symmetries. ...
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152 views

Problem with determining number of goldstone bosons

Consider a theory $$\mathcal{L}=(\partial_\mu\Phi^\dagger)(\partial^\mu\Phi)-\mu^2(\Phi^\dagger\Phi)-\lambda(\Phi^\dagger\Phi)^2$$ where $\Phi=\begin{pmatrix}\phi_1+i\phi_2\\ ...
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2answers
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Bloch Functions as an implication of the Crystallographic Restriction Theorem?

I'm studying Bloch Functions and it seems to me safe to assume that they are the most general Eigenfunction of a Hamiltionian with the crystal periodicity. Now the only considerations made in deriving ...
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591 views

A simple conjecture on the Chern number of a 2-level Hamiltonian $H(\mathbf{k})$?

For example, let's consider a quadratic fermionic Hamiltonian on a 2D lattice with translation symmetry, and assume that the Fourier transformed Hamiltonian is described by a $2\times2$ Hermitian ...
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49 views

How exactly do we know how should transformations of vectors of Hilbert space look like?

There are transformations on physical states which induce unitary transformations of vectors in Hilbert space that correspond to these physical states. We demand that operators in Hilbert space be ...
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62 views

Representation of Lorentz Tranformation on Fields and Wigners theorem

I've been reading about symmetries and I haven't been able piece this information together. I've the Lorentz transformation $$x^\mu \mapsto x^{\rho} = \Lambda_\nu^\mu x^\nu$$ First off, arn't we ...
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1answer
65 views

Does Birkhoff's theorem hold inside the event horizon?

Can Birkhoff's theorem be used to say that the blackhole exterior and interior sections of Kruskal-Szekeres's solution (or coordinate transformations of it like Gullstrand–Painlevé coordinates, etc.) ...
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439 views

Why exactly do sometimes universal covers, and sometimes central extensions feature in the application of a symmetry group to quantum physics?

There seem to be two different things one must consider when representing a symmetry group in quantum mechanics: The universal cover: For instance, when representing the rotation group ...
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48 views

What is conformal symmetry physically?

I'm reading a paper by t'Hooft http://arxiv.org/abs/1410.6675. There is an argument in the paper that I could not understand: "Now that system, described by Maxwell’s equations, does have conformal ...
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49 views

Identifying Lorentz Covariant Equations

Statement: $\phi , A^{\mu}, T^{\mu \nu}$ are a Lorentz scalar, vector, and tensor. Which of the following equations are Lorentz covariant. a. $\phi = A_{0}$ b. $\phi = A^{\mu}A_{\mu}$ c. $\phi = ...
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16 views

Chiral tunneling in Weyl Equation

I am trying to understand perfect tunneling of particles obeying Weyl equation through a potential barrier at normal incidence. I know that this has something to do with chirality, but I am not ...
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29 views

Relation between homotopy theory and symmetry transformation of the Lagrangian

What is the relation between the symmetry transformations of the Lagrangian and homotopy theory? If yes, how? Not sure if this is a math or physics questions. References would be very helpful.
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150 views

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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242 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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22 views

How can intuitively guess what conserved quantities has the system that I am studying?

I'm taking a course in Classical Electrodynamics and in one problem my teacher introduced us to a triplet of fields ($\phi^a$) invariant under internal rotations, i.e. transformations like: ...
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30 views

Implication of rotational symmetry on scattering matrix/ scattering cross-section [closed]

How does the rotational invariance helps simplifying Non-relativistic quantum scattering problems? Is there any any additional information that can be extracted about the scattering amplitude? It ...
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35 views

Free Complex scalar field and conservation principle

In a free complex scalar field, the difference between the number of Particles and antiparticles is conserved. This constarint can be satisfied with a simultaneous creation of equal number of ...
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21 views

Symmetry and present value problems

Suppose we don't know any physical law of nature and we're studying, a system. Let's say a uniformly spherically charged distribution. Now this distribution has the property, that if you rotate this ...
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24 views

Symmetry arguments and plane sheet of charge [duplicate]

The electric field due to a infinite plane sheet of charge is given by $\sigma/\epsilon_o$. Now could we have deduced by symmetry that the electric field's magnitude won't depend on distance?
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95 views

Galilean relativity in QM

Intro I've been trying to show that the generator of boosts can be written in operator form as can be seen here, as: $$ B = \sum_i m_i x_i(t) - t \sum_i p_i $$ As a reminder the transformation ...
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63 views

Why do three-scalar correlation functions vanish by parity?

We have the following Lagrangian: $$ \mathcal L = \frac12 (\partial_\mu \phi)^2 - \frac12 m^2 \psi^2 + \bar\psi(\mathrm i \gamma^\mu \partial_\mu -M) \psi - \mathrm i g \bar\psi \gamma^5 \psi \phi \,. ...
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44 views

What is a Schrödinger background or a Schrödinger symmetry?

In some string theory paper, they mention "Schrödinger background" and "Schrödinger symmetry", which I never heard before. What does that mean?
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1answer
460 views

Does time invariance conclude conservation of energy? [closed]

I find it hard to understand that time-translation invariance necessarily implies conservation of energy. As I understand it, Noether's theorem says that there is an energy conservation because the ...
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1answer
63 views

Symmetry and Group theory book

I would like to start learning about symmetries in physics and how they affect physical quantities. As far as I know, the mathematical language that describes symmetries is the Group Theory. So, I ...
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51 views

Why are Brillouin zones for graphene and monolayers of transition metal dichalcogenides the same?

The geometrical model of graphene is the flat honeycomb lattice, so the Brillouin zone is also flat honeycomb lattice. However, monolayer of transition metal dichalcogenides is not flat as it consists ...
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90 views

What symmetry gives you charge conservation?

This is a popular question on this site but I haven't found the answer I'm looking for in other questions. It is often stated that charge conservation in electromagnetism is a consequence of local ...