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-pnt 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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 9 February 2000 / Accepted: 7 June 2000
Rights and permissions
About this article
Cite this article
Sahlmann, H., Verch, R. Passivity and Microlocal Spectrum Condition. Commun. Math. Phys. 214, 705–731 (2000). https://doi.org/10.1007/s002200000297
Issue Date:
DOI: https://doi.org/10.1007/s002200000297