Coherent structures in strongly interacting many-body systems. II. Classical solutions and quantum fluctuations

Abstract

For pt.I see ibid. vol.22, p.4877 (1989). Previously (I) the author considered a second-quantised Hamiltonian which can be used to model a large number of important strongly interacting many-body systems. He has shown that the dynamics of such systems can be described exactly using quantum fields. The equations of motion derived in this way are highly nonlinear partial differential equations (PDE). He now uses a standard field theoretical approach where initially the fields are treated as classical functions. He studies the solutions of these equations which remarkably, may be obtained making full use of very recent mathematical discoveries (the symmetry reduction method). He finds exact solutions of the equations of motion for the classical field for each of the four main cases separately found in the preceding paper. These cases may correspond to different physical situations and the last, the second-order case, corresponds to the most general physical situation. Subsequently he outlines possible quantisation procedures for these fields. He then briefly discusses the type of boundary conditions which may be applied to both the classical field and the quantum fluctuations which arise.