Quantum corrections to the classical dynamics: application to the SU(2) Lipkin model

We show how nonrelativistic many body techniques can be used to study quantum corrections to the classical limit, in particular to the SU(2) Lipkin model. We show the quantum corrections are essentially of two types: unitary and nonunitary. In this work we perform a detailed study of the unitary corrections. They can be cast in Hamiltonian form and are shown to double the dimension of the effective phase space. As a consequence chaotic behavior emerges. We show that this semiquantal chaos incorporates the Heisenberg uncertainty principle and thus, is the mechanism through which quantum tunneling is effected. We also show that these corrections systematically improve the classical results and propose some quantitative measure of this improvement.