Nonperturbative methods and extended-hadron models in field theory. I. Semiclassical functional methods

This is the first of a series of papers on the use of semiclassical approximations to find particle states in field theory. The meaning of the WKB approximation is examined from a functional-integral approach. Special emphasis is placed on the distinction between a true WKB or semiclassical approach and the weak-coupling approximation to it. Other topics include the center-of-mass motion of particle states and some problems special to field theory such as multiple-particle states, statistics, and infinite-volume systems. Ultraviolet divergences are touched on, but are dealt with more thoroughly in the following paper where specific models are examined. The central result of this series is that certain kinds of nonlinear field theories have extended particle solutions which survive quantization. The most interesting of these objects, which are reminiscent of hadrons, come from theories with spontaneous symmetry breaking.