Aspects of locally covariant quantum field theory

Abstract

This thesis considers various aspects of locally covariant quantum field theory (LCQFT; see Brunetti et al., Commun.Math.Phys. 237 (2003), 31-68), a mathematical framework to describe axiomatic quantum field theories in curved spacetimes. New results include: a philosophical interpretation of certain aspects of this framework in terms of modal logic; a proof that the truncated n-point functions of any Hadamard state of the free real scalar field are smooth, except for n=2; a description of he free Dirac field in a representation independent way, showing that the theory is determined entirely by the relations between the adjoint map, the charge conjugation map and the Dirac operator; a proof that the relative Cauchy evolution of the free Dirac field is related to its stress-energy-momentum tensor in the same way as for the free real scalar field (cf. loc.cit.); several results on the Reeh-Schlieder property in LCQFT, including but not limited to those of our earlier paper; a new and elegant approach to wave front sets of Banach space-valued distributions, which allows easy proofs and extensions of results in the literature.

arXiv commentPhD-thesis, 192 pages, 3 figures, with minor corrections; not available as .dvi or .ps file

References in corpus (1)

• The State Space of Perturbative Quantum Field Theory in Curved Spacetimes

Cited by in corpus (9)

• Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction
• The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor
• Approximate KMS states for scalar and spinor fields in Friedmann-Robertson-Walker spacetimes
• Fermionic fields in the functional approach to classical field theory
• On the Backreaction of Scalar and Spinor Quantum Fields in Curved Spacetimes - From the Basic Foundations to Cosmological Applications
• Remarks on the Reeh-Schlieder property for higher spin free fields on curved spacetimes
• Deformations of quantum field theories on spacetimes with Killing vector fields
• Essential self-adjointness of Wick squares in quasi-free Hadamard representations on curved spacetimes
• The Semiclassical Einstein Equation on Cosmological Spacetimes