Quantum-field-theoretical approach to phase-space techniques: Symmetric Wick theorem and multitime Wigner representation

摘要

In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multitime problems. Analogs of Wick's theorem for the Weyl ordering are verified. Using the Bose- Hubbard chain as an example, we show how these may be applied to constructing a mapping of the system in question to phase space. Regularisation issues and the reordering problem for the Heisenberg operators are addressed. (C) 2014 Elsevier Inc. All rights reserved.