Perturbative Vacuum Wavefunctional for Gauge Theories in the Milne Space

TL;DR

This paper derives the perturbative vacuum wavefunctional for gauge theories in Milne space, providing a foundation for studying vacuum fluctuations relevant to thermalization in heavy ion collisions.

Contribution

It introduces a novel derivation of the Schrödinger functional and vacuum density functional specifically for gauge theories in Milne space, linking it to existing methods.

Findings

Derived the Schrödinger functional for gauge theories in Milne space

Obtained the vacuum density functional and propagators in this setting

Identified the fluctuation spectrum and proved equivalence with symplectic product methods

Abstract

The spectrum of vacuum fluctuations in the Milne space (i.e. the tau-eta coordinate system) is an important ingredient in the thermalization studies in relativistic heavy ion collisions. In this paper, the Schrodinger functional for the gauge theory perturbative vacuum is derived for the Milne space. The Wigner-transform of the corresponding vacuum density functional is also found together with the propagators. We finally identify the fluctuation spectrum in vacuum, and show the equivalence between the present approach and the symplectic product based method.