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Questions tagged [symmetry]

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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Symmetry Argument of a Line Charge

I am been trying to make sense of my professor's lecture notes on where he talks about line charges; in general, I am lost when it comes to the symmetry argument in the case that $E_\phi=0$ on an ...
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53 views

Why impose invariance of the Lagrangian under infinitesimal coordinate transformations?

I am reading Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries by Sylvain Marsat. In section 2B the author imposes the invariance of the ...
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37 views

How is conservation of momentum a consequence of translational symmetry (translational invariance)? [on hold]

If conservation of momentum is a consequence of transnational symmetry, then why we have the condition of conservation of momentum with respect to time i.e. "momentum before collision is same as ...
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46 views

Why does $\Delta^+$ decay into $p$ and $\pi^0$? C P T symmetries

I am not very sure how to check if a decay (or other particle interaction) is possible. I know that one has to check that some quantities (as energy, electric charge, Baryon/Lepton number,...) are ...
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13 views

Does the homogeneity and isotropy of space imply that the expansion of the universe is uniform?

I have asked this question. Now I wonder what could happen if I take a step further. If space is assumed to be BOTH homogeneous AND isotropic, can I prove that the expansion of the universe is uniform?...
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29 views

Why is electric field constant over the charged solid Gaussian sphere?

I saw this example at griffiths. It’s a basic question about gauss’s law but I saw the electric field being treated as a constant and thus, it got outside of the integral. I couldn’t quite understand ...
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2answers
63 views

What do we understand by a force being central?

Gravity is said to be a central force. But the resultant force field of multiple bodies is no longer central as it has many attraction points. My Doubts: Is the idea of a force being central ...
2
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1answer
46 views

Question regarding radial raising/lowering operator for isotropic harmonic oscillator

I understand the symmetry structure of the 3D isotropic harmonic oscillator $H = \frac{\mathbf{P}^2}{2\mu} + \frac{1}{2}m\omega^2\mathbf{X}^2$ as follows. The energy levels are $E_N = \hslash \omega (...
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41 views

Conservation of angular momentum from Noether's theorem and Lorentz invariance

Noether's theorem has been stated in the form that if the assignment $\phi \mapsto \phi + \delta \phi$, $x^{\mu} \mapsto x^{\mu} + \delta x^{\mu} $ leaves the action invariant, then the quantity $$ f^{...
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1answer
52 views

Does the homogeneity of space imply that the expansion of the universe is uniform?

Obviously, homogeneity implies that the density is the same everywhere at any time. However, does this imply that the expansion is uniform? By uniformity, I mean that if I pick three galaxies to form ...
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31 views

Isometry of Riemann sphere?

The complex metric on the Riemann sphere is given in the Wikipedia article to be $$ds^2=\frac{4}{(1+\zeta\bar \zeta)^2}d\zeta d\bar \zeta$$ while the sphere should be mapped to itself under $SL(2,\...
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Classifying all symmetries of a mechanical system [duplicate]

Given a newtonian mechincal system with $n$ objects, we may think of it as living in $\mathbb{R}^{6n+1}$ ; one dimension is time, $3n$ dimensions for velocities, and $3n$ for positions. We then have ...
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55 views

How is a T-violation inherited in a QFT?

CP violation In quantum field theory (QFT), ${\rm CP}$ symmetry or ${\rm CP}$ violation is a property of the Lagrangian. For a ${\rm CP}$ violating QFT, in general, the absolute square of the Feynman ...
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31 views

Action of 1-form symmetry in Maxwell theory

I am reading Lectures on Gauge Theory by David Tong 1. In 3.6.2 first example that the author talk about pure $U(1)$ gauge theory in 4D. In this example, he talk about two 1-form symmetries: electric $...
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84 views

Direct derivation of point-like particle metric in GR

The usual way to derive metric of a point mass in general relativity is (to my knowledge) based on assuming specific form of the metric that reflects spherical symmetry and independence on "time" (...
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24 views

Significance of Wigner-Eckart theorem [duplicate]

What is the physical importance of the Wigner-Eckart theorem and are there any examples of its physical application?
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64 views

How to save time while solving some complex circuit networks?

I know that this platform deals with mainstream physics and the questions raised here must be suitable for a broader community and must not be a specific problem. The questions based on some complex ...
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Can you argue without explicitly calculate the eigenenergies that one Hamiltonian is gapped and another is not?

Consider a pair of one dimensional four band model $H_1$ and $H_2$, which read as: $$ H_1 = \begin{pmatrix}k\sigma_x-E_0&0\\0&k\sigma_x+E_0\end{pmatrix} + \alpha \begin{pmatrix}0&\sigma_x\...
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29 views

Connection between Group of Schrodinger equation and energy level degeneracy [duplicate]

I am recently study group theory and its application in quantum mechanics, but got stuck at a very important point that how group theory can be applied to analyze energy level degeneracy. In many ...
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39 views

Is there a second/many order form of the infinitessimal unitary operator in quantum mechanics?

Is there a second/many order form of the infinitessimal unitary operator in quantum mechanics? We know that a unitarily transformed system must be invariant, i.e. $\langle\psi|\psi\rangle = (\langle\...
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21 views

Supertranslations, superrotations and beyond

Is there any other hidden asymptotic symmetry beyond supertranslations and superrotations? What about superboosts or alike? And super-special transformations analogue to special conformal ...
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19 views

Symmetry v.s. isometry of Minkowski and AdS or dS spacetime

We know some nice spacetime have a lot of symmetries. It is said that Minkowski spacetime has $$ISO(d-1,1)/SO(d-1,1),$$ de Sitter spacetime has $$SO(d,1)/SO(d-1,1)$$ and anti-de Sitter spacetime ...
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29 views

Symmetry of the scattering super-operator

Suppose we have an initial ensemble described by a density matrix $\rho$ and any given member of the ensemble scatters from one of some set of scattering matrices $\{S_g \equiv O_g S O_g^\dagger : g \...
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50 views

Why can we use Gauss' law to show that the field inside a spherical shell is zero?

I've read through the standard explanation of the electric field due to a spherical shell with uniform charge density. This explanation argues that because a Gaussian surface inside the shell encloses ...
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25 views

Strange symmetry of Haldane model edge

In the Haldane model we break both the inversion symmetry and time reversal symmetry, as a consequence I didn't not have any expectations when it comes to symmetry of the energy bands. However, to my ...
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76 views

Simple calculation on coordinate transformation of Lagrangian (Qualls' CFT lecture note)

I have a question while reading "Lectures on conformal field theory" by Qualls (https://arxiv.org/abs/1511.04074). $^1$ Question. I cannot find that the transformation (1.12) makes the action ...
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29 views

Conserved charges generate transformations

Focussing on classical mechanics of a point particle, WLOG since it captures the relevant information for field theory and generalises to the quantum case, how do we show -- in general -- that ...
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41 views

Derivation of Isometries of $AdS_3$ in Poincare Coordinates

We know that $SO(d,2)$ is the isometry group of $AdS_{d+1}$. Let's only consider $AdS_3$ in this question. In Poincare coordinates ($r,t,x)$, these can be grouped as follows : Two translations $$r'=...
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39 views

Symmetry factor of gluon self-energy

In Peskin & Schroeder, p.523, they give the diagram contributing to the gluon self-energy that arises from the 3-gluon vertex, and they claim that the $1/2$ factor is a symmetry factor: How can ...
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35 views

Vanishing Poisson bracket with non-vanishing Moyal bracket

Let $M=\mathbb{R}^{2n}$ be the phase space with standard Poisson bracket on smooth functions on $M$. Fix a classical hamiltonian $h$ (function on $M$) and function $f$ generating symmetry of $h$ i.e. $...
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47 views

Reparametrization invariance in FRW

It is usually pointed out that FRW metric is invariant under time reparametrization. Consider the flat case for simplicity $$ds^2=N(t)^2dt^2-a(t)^2dr^2-a(t)^2r^2d\Omega^2$$ The choice of function $N(...
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53 views

Conflict of domain and endpoints in Noether's theorem and energy conservation

In the derivation of energy conservation, there is the transformation $q(t)\rightarrow q'(t)=q(t+\epsilon)$, whose end points are kind of fuzzy. The original path $q(t)$ is only defined from $t_1$ to $...
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0answers
45 views

Deriving the Lagrangian of a set of interacting particles only from symmetry

In section 5 of Landau and Lifshitz's Mechanics book, they show that the Lagrangian of a free particle must be proportional to its velocity squared, $\mathcal{L} = \alpha\mathbf{v}^2$ using only ...
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1answer
61 views

Scattering states for even potential in 1D

E.g. For a finite square well that has the following potential: $$ V(x)= \begin{cases} 0, & |x|>a \\ -V_0, &|x|\leq a ...
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48 views

Dirac bracket and Poisson bracket, asymptotic symmetry

I am reading the paper arXiv:9906126. https://arxiv.org/abs/gr-qc/9906126 on the symmetry algebra at horizon (see also well known work done by Brown and Henneaux about the asymptotic algebra of AdS$...
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18 views

Rotational invariance of the conductivity tensor (Classical Hall Effect)

In classical Hall effect, the conductivity tensor is given as $\sigma = \frac{\sigma_{DC}}{1+\omega_B^2 \tau^2} \begin{pmatrix} 1 & -\omega_B \tau \\ \omega_B \tau & 1 \end{pmatrix}$ where ...
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1answer
57 views

Translation invariance of point particles as a field theory

The case of point particles, relativistic or not, can be treated as a field theory in general, ie for the $(1+1)$-dimensional case this is the theory of a field theory on the vector bundle $$\pi : \...
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61 views

How to show that translational invariance in $y$ of implies that it's an eigenstate of $p_y$?

Let us consider a particle on a plane with uniform magnetic field $B=B\hat{z}$, and hence with the Hamiltonian $H=\frac{1}{2m}(\vec{p}+e\vec{A})^2$. I am concerned with finding the energy eigenstates, ...
2
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60 views

Gravity in an Earth-sized hole in “solid” outer space [duplicate]

I'm a math PhD student, and far from an expert on physics. If anything is ambiguous or uses the wrong terminology, please correct it or let me know. About a decade ago, a friend gave me a paradoxical ...
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1answer
42 views

Are special conformal transformations continuous?

My understanding of special conformal transformations (SCTs) is fairly limited, but I believe that they are composed of an inversion, a translation and another inversion. Since inversions are discrete ...
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27 views

Does isotropy depend on the location of the origin from where we see the medium?

Let us say we have a charged non-conducting sphere having a spherically symmetrical charge density $\rho (r)$ that decreases as $r$. Ignoring all other properties, If we positon ourselves in the ...
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43 views

Extended objects, bundle description and transformations

In the hope of trying to come up with a clear mental picture for what a transformation is in physics, I encounter some difficulties due to the variety of objects that appear in physics. While no ...
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1answer
144 views

How to check if a generating function produces an identity transformation without substituting the CT equations in the Hamiltonian?

In chapter 9, Goldstein ($3^{rd}$ ed.) includes a discussion and a few "trivial special cases" of Canonical Transformation which keeps the form of the Hamiltonian unchanged and named it Identity ...
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27 views

Solving resistance using symmetry

Recently I've been studying current electricity and I saw many books using symmetry to solve circuits. broadly categorised as left/right symmetry and up/down symmetry where we take current to be ...
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27 views

Is there a specific structure to the automorphism set of a field theory with respect to internal v. spacetime symmetries?

I'm trying to work out what it means exactly for a field to be transformed, without referring to gauges for now. As far as I can tell, from a rigorous perspective, a transformation of the field is an ...
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17 views

Are radial forces always conservative? [duplicate]

Well both gravity and coulombic electrostatic forces are radial forces (acting along the line joining the sources) and their potential energy is defined whereas magnetic force is not radial force and ...
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29 views

A fast and automated way to check if symmetry (space group) operations preserve a lattice

Consider the simple cubic lattice. There are symmetry operations which preserve the lattice symmetry such as translations and rotations around certain axes. There are also symmetry operations that do ...
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71 views

Simple/elementary explanation for $\mathbf{3} \otimes \mathbf{\bar{3}} = \mathbf{8} \oplus \mathbf{1}$? [duplicate]

I am preparing a talk on the Eightfold Way, and am attempting to explain the spectra of the light mesons/baryons via representation theory. It will be delivered to students who have never seen ...
2
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0answers
17 views

Time reversal symmetry of the Faddeev-Popov determinant

I am studying the Faddeev-Popov procedure to quantize a non-Abelian gauge theory, and I got confused by the status of the time reversal symmetry. People have different definitions of the time reversal ...
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2answers
103 views

Naming symmetries in quantum systems, e.g. $\mathbb{Z}_2$ or $U(1)$

I'm constantly confused by some of nomenclature that is associated with symmetries in quantum Hamiltonians and was hoping someone could set me straight. Specifically, we often have something like a ...