The construction of c-number fields and their nonlinear equations of motion for quantum many-body fermion systems

摘要

A k-dependent state has been constructed from two pairs of mutually commuting Fermi-Dirac operators by replacing the Grassmann numbers in the conventional definition of a fermion coherent state. The Heisenberg time-dependent form of this state was then combined with a particular spin state to give a resultant state G], the spin component containing a series of unknown k-dependent weights. A classical c-number field, phi(c),(r, t), was then defined by an expectation value of the quantum field, psi, using G] and an energy and time-dependent phase. It is demonstrated that the form of the equation of motion for phi(c)(r, t) is identical to that for psi. (C) 1998 Elsevier Science B.V. [References: 31]