KMS, etc

Abstract

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 role 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. This paper is dedicated to Huzihiro Araki on the occasion of his seventieth birthday, with admiration, affection and best wishes.

56 pages, submitted to J. Math. Phys

Cited by in corpus (12)

• Massless interacting quantum fields in deSitter spacetime
• Construction of KMS States in Perturbative QFT and Renormalized Hamiltonian Dynamics
• Euclidean Gibbs states of interacting quantum anharmonic oscillators
• Thermal equilibrium states of a linear scalar quantum field in stationary spacetimes
• Spin & Statistics in Nonrelativistic Quantum Mechanics, I
• A note on the Landauer principle in quantum statistical mechanics
• Magnetism and the Weiss Exchange Field - A Theoretical Analysis Inspired by Recent Experiments
• Renormalization Proof for Massive phi_4^4 Theory on Riemannian Manifolds
• Snowmass White Paper: The Quest to Define QFT
• On the relativistic KMS condition for the P(ϕ)_2 model
• Spin - or, actually: Spin and Quantum Statistics
• Boundary conformal fields and Tomita--Takesaki theory