Dynamical C*-algebras and kinetic perturbations

TL;DR

This paper extends the framework of dynamical C*-algebras for scalar fields to include locally perturbed kinetic terms, enabling the description of quantum fields in deformed Minkowski spaces with adjusted causality relations.

Contribution

It introduces an extension of dynamical C*-algebras to incorporate kinetic perturbations, with proofs of Fock space representations satisfying generalized causality.

Findings

Existence of Fock space representations for the extended algebra.

Representation of scalar fields in locally deformed Minkowski spaces.

Validation of generalized causality relations through cohomological arguments.

Abstract

The framework of dynamical C*-algebras for scalar fields in Minkowski space, based on local scattering operators, is extended to theories with locally perturbed kinetic terms. These terms encode information about the underlying spacetime metric, so the causality relations between the scattering operators have to be adjusted accordingly. It is shown that the extended algebra describes scalar quantum fields, propagating in locally deformed Minkowski spaces. Concrete representations of the abstract scattering operators, inducing this motion, are known to exist on Fock space. The proof that these representers also satisfy the generalized causality relations requires, however, novel arguments of a cohomological nature. They imply that Fock space representations of the extended dynamical C*-algebra exist, involving linear as well as kinetic and pointlike quadratic perturbations of the field.