  The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to
study a quantum system by means of an effective classical Hamiltonian -
depending on quantum coupling 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.
