Generalized Wavefunctions for Correlated Quantum Oscillators I: Basic Formalism and Classical Antecedants

TL;DR

This paper introduces a generalized formalism for quantum dynamics of correlated oscillators using classical probability theory extensions, incorporating resonance phenomena and field theory perspectives.

Contribution

It presents a novel approach to quantum dynamics based on quasi-invariant measures and functorial analytic continuation, linking classical probability with quantum correlations.

Findings

Incorporates Breit-Wigner resonances into quantum dynamics.

Uses quasi-invariant measures for classical-quantum transition.

Provides a formalism with natural field theory interpretation.

Abstract

In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space for our description of dynamics. This is based on certain distributions rather than invariant Gibbs measures. The first quantization is by functorial analytic continuation of real probability amplitudes, mathematically effecting the introduction of correlation between otherwise independent subsystems, and whose physical consequence is the incorporation of Breit-Wigner resonances associated to Gamow vectors into our description of dynamics. The resulting quantum dynamics admits a natural field theory interpretation. This basic formalism will be employed in subsequent installments of the series.