An indefinite metric model for interacting quantum fields with non-stationary background gravitation

TL;DR

This paper develops a model of quantum fields with indefinite metrics in curved, non-stationary spacetimes, analyzing their scattering behavior and demonstrating the approach in de Sitter space.

Contribution

It introduces a relativistic Ansatz for quantum field vacuum expectations on curved spacetimes, incorporating non-trivial scattering and gravitational effects with indefinite metrics.

Findings

Constructed local, covariant quantum fields with indefinite metric.

Analyzed scattering behavior and derived the scattering matrix.

Verified the asymptotic condition for de Sitter space.

Abstract

We consider a relativistic Ansatz for the vacuum expectation values (VEVs) of a quantum field on a globally hyperbolic space-time which is motivated by certain Euclidean field theories. The Yang-Feldman asymptotic condition w.r.t. a "in"-field in a quasi-free representation of the canonic commutation relations (CCR) leads to a solution of this Ansatz for the VEVs. A GNS-like construction on a non-degenerate inner product space then gives local, covariant quantum fields with indefinite metric on a globally hyperbolic space-time. The non-trivial scattering behavior of quantum fields is analyzed by construction of the "out"-fields and calculation of the scattering matrix. A new combined effect of non-trivial quantum scattering and non-stationary gravitational forces is described for this model, as quasi-free "in"- fields are scattered to "out"-fields which form a non quasi-free representations of the CCR. The asymptotic condition, on which the construction is based, is verified for the concrete example of de Sitter space-time.