  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.
