Generalized quantum Vlasov equation for particle creation and unitary dynamics

TL;DR

This paper generalizes the quantum Vlasov equation to account for vacuum ambiguities in particle creation due to time-dependent external fields, proposing a new criterion to select the physical vacuum and ensure consistent dynamics.

Contribution

It introduces a generalized quantum Vlasov equation that incorporates different vacuum choices and proposes a stronger criterion than unitarity to reduce quantization ambiguities.

Findings

Generalized quantum Vlasov equation for spatially homogeneous external fields.

Analysis of vacuum ambiguity effects on particle creation.

Proposed a new physical criterion to select the vacuum.

Abstract

The loss of time-translational invariance caused by a time-dependent external agent leads to particle creation effects in quantum field theory. This phenomenon results in ambiguities when selecting the quantum vacuum of the canonical quantization. In this work we analyze how the time evolution of the number of created particles depends on these ambiguities when external agents are spatially homogeneous. In particular, we generalize the standard quantum Vlasov equation in order to accommodate in its formulation the possibility of having different choices of vacuum, including adiabatic vacua. This study leads us to propose a new physical criterion stronger than the unitary implementation of the dynamics in order to reduce the quantization ambiguities.