Abstract
We discuss the loop group G(S1,G) of mappings of the circle S1 into a compact Lie group G. We show that there exists a realization of projective unitary representation of G in the Hilbert space of functionals of holomorphic fields with values in G/sup /C (the complexification of G). We show that this representation belongs to the discrete series of positive energy representations of G We discuss the quantum field theory of holomorphic fields.
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