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Passivity and microlocal spectrum condition

Hanno Sahlmann·Rainer Verch
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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.

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Hanno Sahlmann, Rainer Verch. 2000-02-09. Passivity and microlocal spectrum condition. https://doi.org/10.1007/s002200000297

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