Representations of a local current algebra: Their dynamical determination

Local currents are used to describe nonrelativistic many-body quantum mechanics in the thermodynamic limit. The problem of determining a representation of the local currents corresponding to a given Hamiltonian is studied. We formulate the dynamics in such a way that one solves simultaneously for the ground state and the representation of the local currents. This leads to two coupled functional equations relating the generating functional to a functional which describes the ground state. Together these functionals determine a representation of the local currents in which the Hamiltonian is a well-defined operator. The functional equations are equivalent to a set of integro–differential equations for expansion coefficients of the two functionals.