WKB wave function for systems with many degrees of freedom: A unified view of solitons and pseudoparticles

The WKB method for systems with many degrees of freedom is developed. Using a given imaginary-time (Euclidean) classical solution of the equations of motion, we explicitly construct the WKB wave function in the classically forbidden region of configuration space. Similarly, we construct the wave function for the allowed region using a real-time (Minkowski) solution. For this purpose we use the collective-coordinate method previously developed for solitons in quantum field theory. The present WKB method is an extention of that by Banks, Bender, and Wu to systems with may degrees of freedom and field theories. This paper is intended to present ideas and the general formalism: two applications are briefly discussed: the quantization condition for periodic solutions and vacuum tunneling in field theories.