Quantum Field Theory on Curved Backgrounds

TL;DR

This paper reviews the development of quantum field theory on curved spacetimes, introducing a new functional approach and foundational framework using advanced mathematical tools like microlocal analysis and category theory.

Contribution

It presents a novel formulation of quantum field theory on curved backgrounds based on non-linear functionals, establishing a new foundation for locally covariant classical field theory.

Findings

Develops a new functional approach to quantum fields on curved spacetimes

Integrates microlocal analysis with global analysis and category theory methods

Provides a comprehensive review of the status and mathematical foundations

Abstract

We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally covariant classical field theory. For all that, methods from microlocal analysis combined with some methods from global analysis, namely differentiation on locally convex spaces, and category theory are crucially employed.