The case of a noninteracting infinite Bose gas at zero temperature is studied in the formalism of local current algebras, using the representation theory of nuclear Lie groups. The class of representations describing such a system is obtained by taking an ``N / V limit'' of the finite case. These representations can also be determined uniquely from the solutions of a functional differential equation, which follows in turn from a condition on the ground state vector. Finally a system of functional differential equations is formulated for a theory with interactions, using a proposed definition of indefinite functional integration.
We continue the investigation of the preceding paper into the irreducible representations of local nonrelativistic current algebras. Here, we concentrate on the new features which arise in classifying the representations of the current algebra with regard to particle statistics, and in including internal variables such as spin.
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