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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.

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Good question. The answer is that one can always (completely) symmetrize the integrand with respect to $L!$ loop variables. For instance, the two-loop 1 2 \ x1 / \____ …
answered Nov 19 '16 by Physicsworks