The Interacting Bose Fluid: Path Integral Representations and Renormalization Group Approach

Abstract

We review the various rigorous representations of the boson partition function as an integral over function space. Two approximation schemes for the evaluation of such path integrals are discussed: the saddle point method and the method of the renorma-lization group. These methods are applied to the critical behavior of the interacting Bose fluid. The saddle point method leads naturally to a description of the À transition in terms of quantized vortex lines which create microturbulence in the superfluid. The renormalization group approach leads to the conclusion that the critical behavior of the Bose fluid is identical to that of a classical system of spins with two components.