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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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1answer
149 views

Why do we divide by a symmetry factor the total cross section of scattering?

Srednicki Ch. 11 (p.84) provides an argument for introducing by hand a symmetry factor $S$ in the final integral for the total cross-section. $$ \sigma = \frac1{S} \int d\sigma. \tag{11.36} $$ The ...
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Isotropic moments of inertia

Explicit integration can show that the moment of inertia of a Platonic solid (i.e., tetrahedron, cube, octahedron, dodecahedron, or icosahedron) of uniform density is the same around any axis passing ...
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1answer
46 views

Is the Kerr metric more symmetric than a normal type D spacetime?

The Kerr spacetime is of Petrov type D (see here for the Petrov classification of spacetimes). In the Newman-Penrose formalism, from the Goldberg-Sachs theorem we can conclude that there is a choice ...
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1answer
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What space group describes a 1-dimensional crystal with reflection symmetry along axis?

I'm trying to understand the symmetry of an effectively 1-dimensional system, but I'm confused about how the 1-dimensional ``line groups'' are classified. If you have a system along the $z$-axis which ...
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0answers
15 views

Why is elastic scattering of photons (largely) non-isotropic, but inelastic scattering is isotropic?

I'm working on an experiment regarding Raman spectroscopy, and i'd like to fully understand the reasoning behind this fact. I assume it is related to the photons momentum. My apparatus has a '...
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0answers
50 views

Curvature and Symmetries of spacetime

Is there any relation between symmetries of spacetime and the curvature invariants? For example is spherical symmetric spacetimes, necessarily have positive curvature? Could we define any spherical ...
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1answer
169 views

How is the $E$-field getting canceled between outer and inner surface of a neutral conducting spherical shell?

I am reading Purcell's E&M book and in one of the example questions, it shows that there is no E field between outer and inner surface after a a point charge is located at an arbitrary position ...
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1answer
325 views

Spherical symmetry of Cooper pair wave function

Can someone please explain to me how the wave function of a Cooper pair is spherically symmetric?
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1answer
40 views

Show Lagrangian is invariant under infinitesimal $SO(3)$ transformation

Suppose we have the Lagrangian density for a triplet of real scalar fields, $$ L = \sum_{a=1}^3 \left[ \frac{1}{2}\partial_\mu\phi_a\partial^\mu\phi_a - \frac{1}{2}\phi_a\phi_a \right]. $$ How do ...
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0answers
32 views

Is “gauge” another way of saying “choosing a coordinate system”? [closed]

So far, when I find the term "gauge" it means to choose a convenient coordinate system so a certain condition is satysfied. Is this the general meaning of "gauge"? Or is there something else to it.
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1answer
75 views

How do we know that the actual universe has no Killing vector fields?

This article states the following: The infinitude of conserved energies constructed via Noether’s theorem suffers a startling reversal as soon as Special Relativity is superseded by General ...
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3answers
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(Coming from Wigner's Theorem): What is a Symmetry in QFT?

In classical mechanics, classical field theory and QM, I was introduced to the concept of "Symmetry" as some kind of active transformation of either spacetime / time or configuration space (or of the ...
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1answer
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Showing rotation is a symmetry of given Lagrangian

I have the Lagrangian $L = \frac{1}{2}m(\dot{x}^2+\dot{y}^2) - ax^2 -by^2 -cy^3$. I am trying to work out the conditions that $a,b,c\in\mathbb{R}$ must satisfy so that rotations around the origin, i.e....
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What is the $R$-symmetry group for ${\cal N}=6$ supergravity in $D=4$ dimensions?

What is the $R$-symmetry group for ${\cal N}=6$ supergravity in $D=4$ dimensions?
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1answer
38 views

maximally symmetric spacetime

An empty spacetime has zero or constant Ricci Scalar (depending on the cosmological constant). Is there a theorem which guarantees that such a spacetime should be Minkowski or dS/AdS? In other words, ...
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1answer
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Does Special Relativity Set a Canonical Zero of Energy?

In special relativity, one has the equation $$ E^2 = m^2 + p^2 $$ It seems like this is saying that there is an absolute zero of energy: the energy of a massless, momentumless particle. On the other ...
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Conservation of SU representations [closed]

Out of the symmetries SU(2),SU(3) and SU(6), which is conserved the most in nature? Has any of this symmetries been broken? I ask you because i think that SU(3) is indeed broken since it does not ...
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1answer
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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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Feynman diagrams of $(\phi^{\dagger}\phi)^{2}$-theory up to order 2

I have to compute all diagrams, which contribute to the two-point function at order $\mathcal{O}(\lambda^{2})$ for the interaction $$\mathcal{L}_{int} = -\frac{\lambda}{4}(\phi^{\dagger}\phi)^{2}$$ ...
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Gauge group R and U(1) and a global symmetry

In the beautiful paper by Harlow et Ooguri, they write in section 2.1 about this action $$ S=-\frac12 \int_M F_a \wedge \star F_b \delta^{ab}\;, $$ with index $a=1,2$. They say that if the gauge ...
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1answer
50 views

Irreducible representations

I was studying group theory yesterday and i had this question. If i have an irreducible representation D that belongs in G and another irreducible representation F that belongs in G, is it right to ...
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1answer
64 views

What is the physical meaning of the particle-hole symmetry in condensed matter physics?

It is often mentioned that a mean-field BdG Hamiltonian for a superconductor has the particle-hole symmetry. i.e., if $|\Psi_{\mathbf{k}}\rangle$ is an eigenstate of $H^{BdG}_{\mathbf{k}}$ with ...
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2answers
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What are the generators of spherical symmetry?

The title says it all. I think this should be a pretty simple question but I just couldn't find the answer. Ok -- I'll give a bit more context to my question. I'm encountering this in the context of ...
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1answer
313 views

Spherical conducting shells behaviour

My textbook provides the following problem: Consider a spherical conducting shell with inner radius $R_2$ and outer radius $R_3$, that has other spherical conductor inside it with radius $R_1$ (...
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4answers
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Can conservation of momentum be violated?

The law of the conservation of momentum has been established for hundred of years. Even in Quantum field theory every particle collision must be momentum-conserving if there is homogenity in space. ...
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2answers
344 views

Maximally symmetric spaces

In GR, what is the most precise definition of a maximally symmetric spacetime? Also, we study about the temporal boundary of dS space, and a spatial boundary of AdS space, but aren't these spaces ...
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New symmetries upon quantization

In standard field theory texts, a “classical symmetry” is defined to be a transformation $\phi\to\phi’$ such that the corresponding action is left invariant. The symmetry is said to survive ...
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Conserved charge commutation relation under $SU(2)$ symmetry in two complex Klein-Gordon fields

I'm trying to show that conserved charges of two complex equal-mass Klein-Gordon fields under $SU(2)$ transformation fulfill the following commutation relation: $$ [Q^j, Q^k]=i\epsilon^{jkl}Q^l .$$ I ...
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Why is phason/amplitudon in CDW parity odd/even?

The question is about collective modes of charge density waves, i.e., amplitude and phase fluctuations $\delta,\phi$ of the order parameter $\Delta(x,t)=(\Delta_0+\delta)e^{i\phi}$. I read in many ...
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0answers
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Does gauge fixed string theory have any symmetries?

It is a theorem apparently that quantum gravity theories must have no global symmetries. Yet a theory like Witten's Cubic String Field Theory has guage symmetries. If we fix the guages, this removes ...
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1answer
108 views

Symmetries in QFT preserving only combination of action and measure

Could we list examples of symmetries that preserve only the combination of the measure $\mathcal{D}\phi$ together with $e^{-S}$ but not each on their own? (That is, symmetries which have no classical ...
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1answer
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Evaluation of Commutation Relations in Ballentine's book

I'm reading chapter 3 of Leslie Ballentine's book Quantum Mechanics : A Modern Development but there are a few derivations I don't understand. Question 1 : In the middle of page 74, it says ...
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0answers
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Symmetrical design of a tuning fork [duplicate]

I was reading Ch. 10 of Kleppner and Kolenkow and I came across an explanation which said "The energy loss in a tuning fork is primarily due to heating of the metal. Air friction and energy loss to ...
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2answers
60 views

Confusion about Noether's theorem

In my field theory class we recently derived Noether's theorem: We consider a infinitessimal transformation $\phi \to \phi + \epsilon \,\delta\phi$ of our field which preserves action i. e. $\delta S =...
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1answer
27 views

How to show the that Lorenz gauge is true given that the scalar and the magnetic vector potentials are not unique?

So I understand that we select the divergence of A (magnetic vector potential) to be: $$\frac{1}{c^2}\dot{\phi} + \nabla\cdot\vec{A} = 0.$$ The Lorenz gauge (1). because of the symmetries in ...
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1answer
45 views

Space translation of coordinates, classical field theory

Consider the Lagrangian density $L = -\frac{1}{4}F_{\mu\nu}F^{\mu \nu}$ with $F_{\mu \nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu} $. After deriving the Euler-Lagrange equations for this ...
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2answers
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Why are symmetries in phase space generated by functions that leave the Hamiltonian invariant?

Hamilton's equation reads $$ \frac{d}{dt} F = \{ F,H\} \, .$$ In words this means that $H$ acts on $T$ via the natural phase space product (the Poisson bracket) and the result is the correct time ...
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2answers
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Is there a kind of Noether's theorem for the Hamiltonian formalism?

The original Noether's theorem assumes a Lagrangian formulation. Is there a kind of Noether's theorem for the Hamiltonian formalism?
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1answer
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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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1answer
49 views

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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2answers
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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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1answer
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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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1answer
49 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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1answer
194 views

Is there a sensible fully-discretized Hamilton's principle?

In computational physics it is common to formulate Hamilton's principle in a semi-discrete way, where space is continuous but time is discrete: in other words the Lagrangian $$L(q, \dot q, t): \mathbb{...
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6answers
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Can Noether's theorem be understood intuitively?

Noether's theorem is one of those surprisingly clear results of mathematical calculations, for which I am inclined to think that some kind of intuitive understanding should or must be possible. ...
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1answer
148 views

Isotropy subgroup of a non-zero vector in 3D space

Recentely i got an assignment for a course of group theory applied to physics, in which i had to find the isotropy group of a vector $v=(1,0,0)^T$ under the euclidean group $E=\mathbb{R^3}\ltimes O(3)$...
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1answer
182 views

Symmetry arguments in Magnetostatics

I am not sure that I understand how to argue using symmetry arguments that the magnetic field lies in a certain direction. Say we are given a circular loop of radius $R$ with a steady current $I$ ...
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1answer
240 views

Trying to work out the CP-transformation property of the Higgs potential

The parity transformation property of a complex scalar field $\phi(x)$ is given by: $$P\phi(t,\textbf{x}) P^{-1}=\eta_P\phi(t,-\textbf{x})$$ where $\eta_P=\pm 1$. The charge conjugation property of a ...
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1answer
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Why is electric field constant over the charged solid Gaussian sphere? [closed]

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
65 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 ...