Passivity and microlocal spectrum condition

Details Passivity and microlocal spectrum condition Passivity and microlocal spectrum condition

2000-02-08

arxiv.org/abs/math-ph/0002021v2

Commun.Math.Phys. 214 (2000) 705-731

Physics

Mathematical Physics

latex2e, 29 pages. Change in references, typos removed

Scientific paper

10.1007/s002200000297

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.

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