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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### (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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
49 views