  A modification of the Holstein-Primakoff transformation is proposed such that
creation and annihilation operators for a bosonic field are rewritten as
operators of a $SU(2)$ algebra. Once it is applied to a quantum Hamiltonian, a
subsequent application of the prescription by Lieb to obtain the classical
limit for spin operators allows one to write efficiently a classical
Hamiltonian for the system. This process is illustrated for the $M$-atom
Jaynes-Cummings model.
