Zero-point oscillations, local stability, and the effective action

We define a gauge-invariant action functional for non-Abelian gauge theories by deriving 't Hooft's generating functional from the vacuum-to-vacuum transition amplitude, and we explicitly demonstrate its gauge-invariance properties. We then examine the effective action in the loop expansion and show that in the presence of a nonvanishing background field the unrenormalized one-loop term can be written as the change in the zero-point energy of the theory. Finally, we consider the interpretation of an imaginary part of the effective action and its relation to local stability by examining the source of such an imaginary part within the Euclidean theory