Refined Algebraic Quantization and Quantum Field Theory in Curved Space-Time

TL;DR

This paper applies refined algebraic quantization to scalar fields in curved space-time, establishing a framework for Fock representations that accommodate particle creation phenomena.

Contribution

It introduces a rigorous method for constructing Fock representations in curved space-time using refined algebraic quantization, addressing physical relevance.

Findings

Unique Fock representation derived for scalar fields in curved space-time.

Construction of in- and outgoing state representations consistent with particle creation.

Identification of unphysical quasifree states in the general construction.

Abstract

Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The construction can be made rigorous for a general globally hyperbolic space-time, but the quasifree state so obtained turns out to be unphysical in general. We exhibit a closely related pair of Fock representations that is also defined generically and conforms to the notion of in- and outgoing states in those situations where particle creation by the external field is expected.