# Quantum fields obtained from convoluted generalized white noise never have positive metric

June 03, 2015

It is proven that the relativistic quantum fields obtained from analytic
continuation of convoluted generalized (L\'evy type) noise fields have positive
metric, if and only if the noise is Gaussian. This follows as an easy
observation from a criterion by K. Baumann, based on the
Dell'Antonio-Robinson-Greenberg theorem, for a relativistic quantum field in
positive metric to be a free field.

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