AQFT on curved spacetimes

entry to be merged or else disambiguated with locally covariant perturbative quantum field theory



algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)



field theory: classical, pre-quantum, quantum, perturbative quantum

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT




From the physical point of view there are two different reasons to consider the Haag-Kastler approach on more general spacetimes than the Minkowski spacetime:

  • It is expected that such a theory, while not solving the problem to construct a theory of quantum gravity, would still have a wide range of validity.

  • From a conceptual viewpoint abandoning the special situation of Minkowski spacetime could lead to the development of new ideas and tools that turn out to be helpful to understand the concept of a quantum field theory better.

The first point deserves some elaboration: The curved manifolds under consideration are supposed to be solutions to the field equations of General Relativity, i.e. physically realistic spacetimes, so that gravity is modelled classically by the curvature of spacetime. A quantum field theory on such a spacetime should be able to model the situation of elementary particles that feel the effects of gravity while neglecting the effect that the particles themselves have on spacetime (the notion of “particle” is highly nontrivial and problematic in this setting and is to be understood in a metaphorical sense in the given context).

Example: If you let an electron drop from your hand to the ground, that would be a situation that the theory is supposed to describe. While a full theory of quantum gravity still eludes us, a theory of quantum fields on curved spacetimes could be useful as a kind of interpolation. In a certain sense this is already the case, since the laws of black hole thermodynamics were first discovered with the help of this setting.


Vacuum energy and Cosmological constant

The renormalization freedom in perturbative quantization of gravity (perturbative quantum gravity) induces freedom in the choice of vacuum expectation value of the stress-energy tensor and hence in the cosmological constant.

Review includes (Hack 15, section 3.2.1).

For more see at cosmological constant here.


Gereneral accounts of (perturbative, algebraic) quantum field theory on curved spacetimes includes

Foundations for perturbative quantum field theory on curved spacetimes in terms of causal perturbation theory were laid in

The AQFT-style axiomatization via local nets on a category of Lorentzian manifolds (locally covariant perturbative quantum field theory) is due to

Reviews with emphasis on this AQFT-point of view include

Papers about the application of microlocal analysis include

  • Alexander Strohmaier, Rainer Verch, Manfred Wollenberg: Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and Reeh-Schlieder theorems (arXiv).

Discussion of renormalization in AQFT on curved spacetimes includes

Discussion of the cosmology in the context of AQFT on curved spacetimes includes

Revised on February 9, 2018 09:35:36 by Urs Schreiber (