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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.

1 vote
1 answer
174 views

Question about global internal $SO(n)$ symmetry

I have the following Lagrangian (density) for bosons $$L = \partial_{\mu} \phi^i \partial^{\mu}\phi^i+ m^2\phi^i \phi^i$$ and I am trying to understand why this Lagrangian is invariant under globa …
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2 votes
0 answers
223 views

What is the difference between the groups $PSU(N)$ and $SU(N)$? [closed]

What is the difference between the groups $PSU(N)$ and $SU(N)$? For example how is $PSU(2,2|4)$ different than $SU(2,2|4)$?
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26 votes
3 answers
4k views

Diffeomorphism group vs. $\operatorname{GL}(4,\mathbb{R})$ in General Relativity

specific it says that A more modern interpretation of the physical content of the original principle of general covariance is that the Lie group $\operatorname{GL}(4,R)$ is a fundamental "external" symmetry
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