Heisenberg-picture approach to the evolution of the scalar fields in an expanding universe

TL;DR

This paper develops a Heisenberg-picture framework to analyze quantum scalar field evolution in an expanding universe, including initial states and perturbative fluctuations, with applications to cosmological quantum fields.

Contribution

Introduces a Heisenberg-picture method for quantum scalar fields in expanding universes, handling various initial states and renormalization within a unified approach.

Findings

Calculated Wightman and two-point functions for scalar fields.

Analyzed quantum fluctuations and their evolution.

Discussed renormalization of field equations in cosmological context.

Abstract

We present the Heisenberg-picture approach to the quantum evolution of the scalar fields in an expanding FRW universe which incorporates relatively simply the initial quantum conditions such as the vacuum state, the thermal equilibrium state, and the coherent state. We calculate the Wightman function, two-point function, and correlation function of a massive scalar field. We find the quantum evolution of fluctuations of a self-interacting field perturbatively and discuss the renormalization of field equations.