Deformations of Quantum Field Theories on Curved Spacetimes

TL;DR

This paper extends the deformation of quantum field theories via warped convolutions to curved spacetimes, demonstrating wedge localization and non-isomorphism in models like the Dirac field and de Sitter space.

Contribution

It generalizes warped convolution deformations to globally hyperbolic curved spacetimes with spacelike Killing vectors, and explores their effects on various quantum field theories.

Findings

Deformed fields remain localized in wedge regions.

Deformations produce models non-isomorphic to original theories.

Explicit example with deformed free Dirac and scalar fields.

Abstract

The construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of globally hyperbolic spacetimes. First, we show that any four-dimensional spacetime which admits two commuting and spacelike Killing vector fields carries a family of wedge regions with causal properties analogous to the Minkowski space wedges. Deformations of quantum field theories on these spacetimes are carried out within the operator-algebraic framework - the emerging models share many structural properties with deformations of field theories on flat spacetime. In particular, deformed quantum fields are localized in the wedges of the considered spacetime. As a concrete example, the deformation of the free Dirac field is studied. Second, quantum field theories on de Sitter spacetime with global U(1) gauge symmetry are deformed using the joint action of the internal symmetry group and a one-parameter group of boosts. The resulting theories turn out to be wedge-local and non-isomorphic to the initial one for a class of theories, including the free charged Dirac field. The properties of deformed models coming from inclusions of CAR-algebras are studied in detail. Third, the deformation of the scalar free field in the Araki-Wood representation on Minkowski spacetime is discussed as a motivating example.