Quantum properties of a non-Gaussian state in the large-N approximation
  We study the properties of a non-Gaussian density matrix for a O(N) scalar
field in the context of the incomplete description picture. This is of
relevance for studies of decoherence and entropy production in quantum field
theory. In particular, we study how the inclusion of the simplest non-Gaussian
correlator in the set of measured observables modifies the effective (Gaussian)
description one can infer from the knowledge of the two-point functions only.
We compute exactly the matrix elements of the non-Gaussian density matrix at
leading order in a 1/N-expansion. This allows us to study the quantum
properties (purity, entropy, coherence) of the corresponding state for
arbitrarily strong nongaussianity. We find that if the Gaussian and the
non-Gaussian observers essentially agree concerning quantum purity or
correlation entropy, their conclusion can significantly differ for other, more
detailed aspects such as the degree of quantum coherence of the system.
