# Passivity and microlocal spectrum condition

February 08, 2000

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.

Keywords:

*none*