QFT on curved spacetimes: axiomatic framework and examples

Abstract

In this overview article we present a formalism suitable for constructing models of QFT's on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the standard QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.

54 pages, a review written for the Journal of Mathematical Physics. In this version, typos corrected

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• Linear stability of semiclassical theories of gravity
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• Coordinate space representation for renormalization of quantum electrodynamics
• The Sine-Gordon QFT in de Sitter spacetime
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• Thermal state with quadratic interaction
• Local operators in the Sine-Gordon model: ${\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ and the stress tensor
• On the Cauchy problem for the Fadaray tensor on globally hyperbolic manifolds with timelike boundary
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• Global Hyperbolicity and Self-adjointness