Trace Formulas, a Golden–Thompson Inequality and Classical Limit in Boson Fock Space

Trace formulas for the heat semi-groups of second quantization operators and their perturbations in the abstract boson Fock space are given in terms of path (functional) integral representations. As applications, an inequality of Golden–Thompson type and a classical limit are derived for the trace of the heat semi-group of a perturbed second quantization operator. The abstract results are applied to a model ofP(φ)-type in quantum field theory.