Functional Integral and Stochastic Representations for Ensembles of Identical Bosons on a Lattice

Abstract

Regularized coherent-state functional integrals are derived for ensembles of identical bosons on a lattice, the regularization being a discretization of Euclidian time. Convergence of the time-continuum limit is shown for various discretized actions. The focus is on the integral representation for the partition function and expectation values in the canonical ensemble. The connection to the grand-canonical integral, and a number of differences, are discussed. Uniform bounds for covariances are proven, which simplify the analysis of the time-continuum limit and can also be used to analyze the thermodynamic limit. The relation to a stochastic representation by an ensemble of interacting random walks is made explicit, and its modifications in presence of a condensate are discussed.

42 pages

References in corpus (6)

• Constructive ${\varphi }^4$ field theory without tears
• Universality of the Hall conductivity in interacting electron systems
• Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems
• A variational formula for the free energy of an interacting many-particle system
• Clustering of fermionic truncated expectation values via functional integration
• Complex Bosonic Many-body Models: Overview of the Small Field Parabolic Flow