Quantum Field Theory in a Symmetric Curved Space from a Second Quantization on a Group

TL;DR

This paper introduces a second quantization scheme within a group approach to quantization, tailored for highly symmetric curved spacetimes like Anti-de Sitter, improving vacuum state characterization without requiring global hyperbolicity.

Contribution

It develops a novel second quantization method suited for symmetric phase spaces, extending quantum field theory to curved spacetimes such as Anti-de Sitter space.

Findings

Constructed a QFT on Anti-de Sitter space

Enhanced vacuum state characterization in curved spacetime

Avoided need for global hyperbolicity in the framework

Abstract

In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum Field Theory (QFT) for ordinary relativistic linear fields. We emphasize, among its main virtues, greater suitability in characterizing vacuum states in a QFT on a highly symmetric curved space-time and the absence of the usual requirement of global hyperbolicity. This can be achieved in the special case of the Anti-de Sitter universe, on which we explicitly construct a QFT.