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A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. Examples include the $U(1)$-symmetric quantum electrodynamics and other Yang-Mills theories wherein non-Abelian groups replace the $U(1)$ gauge group of QED.

4
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If $P^{a}$ are finite-dimensional matrices, then I found that your algebra actually implies that $P^{a}=0$. I think that it is a consequence of the fact that $SU\left( N\right) $ is a simple group, …
answered Aug 2 '13 by Grisha Kirilin
6
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The well known property of the harmonic coordinates is that the covariant divergence of a vector field and the d'Alambertian of a scalar field take a particularly simple form: $$ D_{\mu}A^{\mu} \right …
answered Jul 30 '12 by Grisha Kirilin