# Questions tagged [symmetry]

Symmetries play a big role in modern physics and have been a source of powerful tools and techniques for understanding theories and their dynamics. 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 forms a group, and the name of this group is used as the name of the symmetry of the object.

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### Why $SU(N)$ and not $U(N)$?

I am going through one example where they introduce the lagrangian density L(x) = \sum_{i = 1}^N \partial^\mu \phi_i^* \partial_\mu \phi_i - m^2 \phi_i^* \phi_i = \partial^\mu \Phi^\...
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### Does rotational symmetry imply reflection symmetry for electrostatic interactions?

Consider two charge distributions $\rho_A(\mathbf{x})$ and $\rho_B(\mathbf{x})$. Suppose that the ground state energy of a system of $n$ electrons in a potential generated by the sum of these two ...
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### The different choises of a metric with the next form: $ds^{2}=-Adt^2+Bdr^2+Cd\Omega^2$

In some papers the starting point is a metric with the next form: $$ds^{2}=-A(t,r)^{2}dt^{2}+B(t,r)^{2}dr^{2}+r^{2}d\Omega^{2}.$$ Like in the Schwarzschild metric where they choice A=exp and B=exp ...
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### Parity transformation of the $\pi^{0}\rightarrow\gamma\gamma$ process

I want to prove that the amplitude $$\mathcal{M}^{\mu\nu}=\epsilon^{\mu\nu\alpha\beta}q_{1\alpha}q_{2\beta}$$ is violating parity. Here $q_{i=1,2}$ are the external momenta of the photons. The total ...
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### Potential of Monolayer Graphene as a High-Precision Cutting Material

"I am exploring the use of monolayer graphene as a cutting material for high-precision applications. We know that graphene has exceptional mechanical properties, such as high strength and ...
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### Is the FRW metric, based on spatial homogeneity and isotropy, rotationally and translationally invariant? If so, how?

The spatial part of the Minkowski metric, written in the Cartesian coordinates, $$d\vec{ x}^2=dx^2+dy^2+dz^2,$$ is invariant under spatial translations: $\vec{x}\to \vec{x}+\vec{a}$, where $\vec{a}$ ...
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### Designing a thought experiment on Noether's Theorem [closed]

By Noether's theorem, in classical physics, conservation of total momentum of a system is result of invariance of physical evolution by translation. So logic says "if" there exists closed ...
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### Does all symmetry breaking have corresponding unitary group?

In high energy physics. Symmetry breaking like electroweak's has corresponding $SU(2)\times U(1)$ unitary gauge group broken down to $U(1)$. Does it mean all kinds of symmetry breaking (even low ...
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