Classical dynamics of quantum fluctuations

TL;DR

This paper introduces a novel classical-like path-based framework to describe quantum fluctuations in weakly interacting quantum field theories, capturing quantum dynamics through stochastic classical paths.

Contribution

It proposes the concept of pseudoclassical paths to represent quantum fluctuations and demonstrates their use in modeling the dynamics of collective observables without external environments.

Findings

Quantum vacuum states can be represented by incoherent classical paths.

Quantum fluctuations of collective observables follow classical stochastic processes.

The formalism differs from coherent state approaches.

Abstract

It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with constrained initial conditions. We call such paths "pseudoclassical" paths and use them to define the dynamics of quantum fluctuations. Every physical observable is assigned a time-dependent value on each path in a way that respects the uncertainty principle, but in consequence, some of the standard algebraic relations between quantum observables are not necessarily fulfilled by their time-dependent values on paths. We define "collective observables" which depend on a large number of independent degrees of freedom, and show that the dynamics of their quantum fluctuations can be described in terms of unconstrained classical stochastic processes without reference to any additional external system or to an environment. Our analysis can be generalized to states other than the vacuum. Finally, we compare our formalism to the formalism of coherent states, and highlight their differences.