2002/04/10 by L. Birke, Lothar Birke, Jürg Fröhlich +1 · 1 citation
Mathematics · Physics and Astronomy · #Connection (principal bundle) #Cosmology and Gravitation Theories #Geometry #Hawking #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum field theory #Quantum mechanics #Realization (probability) #Theoretical physics #Unitary state #Unruh effect #math-ph #math.MP
paper · pdf · doi:10.1142/s0129055x02001442
published as Rev.Math.Phys. 14 (2002) 829-872 · 56 pages, submitted to J. Math. Phys
arxiv created 2002/04/10 · openalex publication_date 2002/07/01 · arxiv updated 2009/11/30 · openalex created_date 2020/07/02 · openalex updated_date 2026/08/05
A general form of the "Wick rotation", starting from imaginary-time Green functions of quantum-mechanical systems in thermal equilibrium at positive temperature, is established. Extending work of H. Araki, the rôle of the KMS condition and of an associated anti-unitary symmetry operation, the "modular conjugation", in constructing analytic continuations of Green functions from real- to imaginary times, and back, is clarified. The relationship between the KMS condition for the vacuum with respect to Lorentz boosts, on one hand, and the spin-statistics connection and the PCT theorem, on the other hand, in local, relativistic quantum field theory is recalled. General results on the reconstruction of local quantum theories in various non-trivial gravitational backgrounds from "Euclidian amplitudes" are presented. In particular, a general form of the KMS condition is proposed and applied, e.g., to the Unruh- and the Hawking effects.