Functional methods in nonrelativistic field theories

Functional methods are developed for nonrelativistic systems containing a single species of interacting particles. These methods are used to illustrate the nonrelativistic analog of the Goldstone theorem and to examine the finite-temperature behavior of several nonrelativistic field theories. The nonrelativistic analog of the negative-mass-term phi4 theory is shown to exhibit a first-order phase transition as well as metastable superheated and supercooled states. The continuum form of Dyson's theory of spin waves is shown to undergo spontaneous breakdown of symmetry at a finite temperature so that the number of spin waves remains constant and the propagator becomes short-ranged. Several extensions of this work are suggested