# 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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### What is the Lie group of gravity?

If the lie group of the three gauge forces are $SU(3)×SU(2)×U (1)$, then what is the symmetry group of gravity? $SL(2,C)$? Just a newbie in Lie groups.
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### Are gravitons Goldstone bosons?

This question is inspired by Are Photons Goldstone Bosons?. And recently in Generalized Global Symmetries, photon was interpreted as Goldstone boson for generalized symmetry (see also my answer for ...
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### Poisson Bracket of a Quantity Involving a Differential

I am working through Warren Siegel's "Fields" and have come across the following exercise on p. 58 involving an action measure and a symmetry generator: Exercise IA4.1. For general variables ...
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### mirror symmetry of spin-1/2 wavefunction: Definition of the reflection operator

I would expect from a reflection operator $\hat{M}$ to leave a wavefunction unchanged if two times applied, thus $\hat{M}^2=1$. However, for a spin-1/2 particle this is not the case when following the ...
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### The radiative modes of an asymptotically flat spacetime and the symmetries

In Ashtekar's paper, the radiative degrees of freedom of an asymptotic flat spacetime in general relativity are obtained. These degrees of freedom live on the null infinity $\mathscr I$, given by the ...
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### Role of isotropy argument in fixing the form of $T^\mu_\nu$ of cosmology (Padmanabhan's book)

The following lines from Gravitation Foundation and Frontiers by T. Padmanabhan (he uses Latin indices for spacetime and Greek indices for space, which is unusual) The assumption of isotropy ...
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### Does the space group P63/m (No. 176) have C6 rotation symmetry?

Recently I'm working on a compound with space group P63/m. The top view of its structure is shown below (where only atoms of z=1/4 are shown). From the list of space groups (Wiki: List of Space ...
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### Why is the symmetry of measurements in SR no longer valid in GR?

In special relativity, we know that if an inertial observer $A$, having a relative motion WRT an inertial observer $B$, attributes, say, time dilation and length contraction to respectively $B$'s ...