Passivity and microlocal spectrum condition
Mathematical Physics
2009-10-31 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Abstract
In the setting of vector-valued quantum fields obeying a linear wave-equation in a globally hyperbolic, stationary spacetime, it is shown that the two-point functions of passive quantum states (mixtures of ground- or KMS-states) fulfill the microlocal spectrum condition (which in the case of the canonically quantized scalar field is equivalent to saying that the two-point function is of Hadamard form). The fields can be of bosonic or fermionic character. We also give an abstract version of this result by showing that passive states of a topological *-dynamical system have an asymptotic pair correlation spectrum of a specific type.
Cite
@article{arxiv.math-ph/0002021,
title = {Passivity and microlocal spectrum condition},
author = {Hanno Sahlmann and Rainer Verch},
journal= {arXiv preprint arXiv:math-ph/0002021},
year = {2009}
}
Comments
latex2e, 29 pages. Change in references, typos removed