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

Abstract

A k-dependent state has been constructed from two paris 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, φ( r, t), was then defined by an expectation value of the quantum field, ψ, using | G〉 and an energy and time-dependent phase. It is demonstrated that the form of the equation of motion for φ c ( r, t) is identical to that for ψ.