Coherent state path integrals in the continuum

TL;DR

This paper develops a consistent formalism for time-continuous path integrals in the coherent states basis, enabling exact results and providing a foundation for advanced approximation techniques in quantum field theory involving bosonic Hamiltonians.

Contribution

It introduces an inconsistency-free approach to continuum coherent state path integrals, facilitating both exact solutions and the development of perturbative and non-perturbative methods.

Findings

Reproduces known exact results in the continuum

Establishes a consistent formalism for path integrals

Lays groundwork for advanced approximation techniques

Abstract

We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set the basis to develop perturbative and non-perturbative approximations already known in the quantum field theory community. These techniques can be proven useful in a great variety of problems where bosonic Hamiltonians are used.