Quantum Field Theory on Curved Backgrounds

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.

19 pages, submitted for the Proceedings of the Kompaktkurs "Quantenfeldtheorie auf gekruemmten Raumzeiten" held at Universitaet Potsdam, Germany, in 8.-12.10.2007, organized by C. Baer and K. Fredenhagen

References in corpus (1)

• Renormalized Quantum Yang-Mills Fields in Curved Spacetime

Cited by in corpus (18)

• Quantum Field Theory on Curved Backgrounds -- A Primer
• Self-dual noncommutative ϕ^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
• Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?
• Approximate KMS states for scalar and spinor fields in Friedmann-Robertson-Walker spacetimes
• Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
• Endomorphisms and automorphisms of locally covariant quantum field theories
• The generalised principle of perturbative agreement and the thermal mass
• On the algebraic quantization of a massive scalar field in anti-de-Sitter spacetime
• Algebraic Structure of Classical Field Theory: Kinematics and Linearized Dynamics for Real Scalar Fields
• Shifted Landau levels in curved graphene sheets
• Dynamical locality of the nonminimally coupled scalar field and enlarged algebra of Wick polynomials
• Influence of quantum matter fluctuations on geodesic deviation
• Snowmass White Paper: The Quest to Define QFT
• A new class of Fermionic Projectors: Møller operators and mass oscillation properties
• The classical limit of a state on the Weyl algebra
• Relative entropy and entropy production for equilibrium states in pAQFT
• Categorial subsystem independence as morphism co-possibility
• On Adiabatic Renormalization with a Physically Motivated Infrared Cut-Off