A new path integral representation for the thermal partition function

Abstract

The boundary conditions corresponding to the Matsubara formalism for the $T > 0$ partition function may be introduced as {\em constraints} in the path integral for the vacuum amplitude. We implement those constraints with time-independent Lagrange multipliers and, by integrating out the original fields, we obtain an alternative representation for the partition function, in terms of the Lagrange multipliers as dynamical fields. The resulting functional integral has the appealing property of involving only $d$-dimensional, {\em time independent} fields, and looks like a nonlocal version of the classical partition function. We develop this formalism within the context of the scalar and Dirac fields.