I find that many authors write the Yang-Mills action as follows: $$\mathcal{J}= \int \operatorname{Tr}(F \wedge \star F).$$ I have yet to find a formal description of the symbol $\operatorname{Tr}$ and am especially interested in its relation to differential geometry. How should I understand it?
What does the symbol $\operatorname{Tr}$ in the Yang-Mills action mean?
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differential-geometry
mathematical-physics
quantum-field-theory
gauge-theory