Fermionized bosons and Szegö's theorem.

Abstract

It is discussed how the bosonic zero-mode operator {ital q} in two-dimensional quantum field theory should be expressed in terms of fermion operators. Two expressions for {ital q} are proposed, one of which is of a clear meaning and the other of a formal nature. The idea of the boson-fermion correspondence is applied to prove simply Szegoe's theorem on an infinite Toeplitz determinant. It is also seen that a fermion theoretical discussion of a special case of the Toeplitz determinant yields a generalization of Szegoe's result.