Effective Hamiltonian with holomorphic variables

The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian – depending on and temperature – and classical-like expressions for the averages of observables. In this work the PQSCHA is derived in terms of the holomorphic variables connected to a set of bosonic operators. The holomorphic formulation, based on the path integral for the Weyl symbol of the density matrix, makes it possible to approach directly general Hamiltonians given in terms of bosonic creation and annihilation operators.