Nonrelativistic Quantum Mechanics Formulated in Terms of Currents

Abstract

The nonrelativistic quantum mechanics of interacting spinless bosons or fermions is formulated in terms of particle and current densities. Natural physical requirements on the structure of the physical states allow one to construct explicitly the physical Hilbert space, and to construct annihilation and creation operators for either bosons or fermions. The problem of extending such methods to the relativistic case is discussed.