Non-classical configurations in Euclidean field theory as minima of constrained systems

Abstract

We study a systematic method of applying the semiclassical approximation to Euclidean field theory. First, we extract generalized collective coordinates which are not in general zero modes. We then apply the semiclassical approximation to the other degrees of freedom by minimizing the action with constraints. Hence we are using configurations which are not classical solutions of the original system. After Gaussian integration we are left with a truncated system, involving only the collective coordinates, with non-trivial dynamics. In particular, this is a clear-cut way to introduce multi-instanton or meron-type configurations. The collective coordinates should be chosen such that their dynamics are a good approximation to the original system for the physical phenomenon considered; a familiar concept in other branches of physics with many degrees of freedom. The formalism leads naturally to the introduction of dynamics in an extra time evolution; in particular cases, we show that this is a very powerful tool. In this paper, we only discuss general ideas and formalisms. Specific applications are postponed to to later publications.