Particle Interpretations and Green Functions for a Free Scalar Field

TL;DR

This paper advances the formalism for defining particles in quantum field theory on curved spacetime, clarifying the relationship between key objects and Green functions, and reformulating particle definitions in a base-independent manner.

Contribution

It develops the Ashtekar and Magnon formalism, relating complex structures to Green functions and expressing particle transformations using directly derivable quantities.

Findings

Derived composition laws for Green functions.

Reformulated particle definitions in a base-independent framework.

Connected complex structures with Green functions.

Abstract

The formalism of Ashtekar and Magnon \cite{AshtekarMagnon:1975} for the definition of particles in quantum field theory in curved spacetime is further developed. The relation between basic objects of this formalism (e.g., the complex structure) and different Green functions is found. It allows one to derive composition laws for Green functions. The relation of two definitions of particles is reformulated in the formalism and the base-independent Bogoljubov transformation is expressed using quantities which are derivable directly from the ``in-out'' Green function.