A note on the boson-fermion correspondence and infinite dimensional groups

Abstract

We show how to construct irreducible projective representations of the infinite dimensional Lie group Map (S1,\(\mathbb{T}\)), by embedding it into the group of Bogoliubov automorphisms of the CAR. Using techniques of G. Segal for extending certain representations of Map (S1, SU(2)) we show that our representations extend to give representations of a certain infinite dimensional superalgebra. We relate our work to the well known boson-fermion correspondence which exists in 1+1 dimensions.