On the role of coherent states in quantum foundations

TL;DR

This paper explores how coherent states serve as a bridge between classical and quantum physics, leading to new insights into phase space path integrals, the relationship between classical and quantum formalisms, and solving complex nonlinear quantum field models.

Contribution

It introduces a natural formulation of phase space path integrals using coherent states and demonstrates the classical formalism as a subset of quantum formalism, solving previously insoluble nonlinear quantum field models.

Findings

Unified classical and quantum formalism via coherent states

New formulation of phase space path integrals

Analytic solutions to nonlinear quantum field models

Abstract

Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that useful connections arise among them. The topics discussed are: (1) a truly natural formulation of phase space path integrals; (2) how this analysis implies that the usual classical formalism is ``simply a subset'' of the quantum formalism, and thus demonstrates a universal coexistence of both the classical and quantum formalisms; and (3) how these two insights lead to a complete analytic solution of a formerly insoluble family of nonlinear quantum field theory models.