nLab
AQFT on curved spacetimes

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

Contents

Idea

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.

References

Gereneral accounts of (perturbative) quantum field theory on curved spacetiems includes

  • N.D. Birrell, P.C.W.Davies, Quantum Fields in Curved Space, Cambridge: Cambridge University Press, 1982

  • Robert Wald, Quantum field theory in curved spacetime and black hole thermodynamics. Univ. of Chicago Press 1994 (ZMATH entry).

  • Stefan Hollands, Robert Wald, Quantum fields in curved spacetime, Physics Reports Volume 574, 16 April 2015, Pages 1-35 (arXiv:1401.2026)

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 standard model of cosmology in the context of AQFT on curved spacetimes is in

Revised on August 8, 2017 13:11:58 by Urs Schreiber (94.220.75.2)