Representations of Local Nonrelativistic Current Algebras

In this paper we show how to specify the particle content of a nonrelativistic quantum theory of $N$ identical spinless particles in terms of observables like the particle number density and the flux density of particles. Our approach to this problem is through a study of the irreducible representations of the local, equal-time current algebra. It is shown how these representations define a functional representation of the current algebra, and that the Hamiltonian can be written in terms of the currents in a nonsingular fashion in any irreducible representation.