Quantization of linearized gravity in cosmological vacuum spacetimes

TL;DR

This paper develops a rigorous algebraic quantum field theory framework for quantizing linearized Einstein gravity with a cosmological constant in cosmological vacuum spacetimes, addressing classical solution structure and observables.

Contribution

It provides a systematic and rigorous quantization approach for linearized gravity in cosmological spacetimes, extending algebraic quantum field theory methods.

Findings

Established conditions for symplectic product non-degeneracy

Analyzed the separation of solution space by classical observables

Extended algebraic quantization techniques to linearized gravity

Abstract

Linearized Einstein gravity (with possibly nonzero cosmological constant) is quantized in the framework of algebraic quantum field theory by analogy with Dimock's treatment of electromagnetism [Rev. Math. Phys. 4 (1992) 223--233]. To achieve this, the classical theory is developed in a full, rigorous and systematic fashion, with particular attention given to the circumstances under which the symplectic product is weakly non-degenerate and to the related question of whether the space of solutions is separated by the classical observables on which the quantum theory is modelled.