  The boson-fermion correspondence of type A is an isomorphism between two
super vertex algebras (and so has singularities in the operator product
expansions only at $z = w$). The boson-fermion correspondence of type B plays
similarly important role in many areas, including representation theory,
integrable systems, random matrix theory and random processes. But the vertex
operators describing it have singularities in their operator product expansions
at both $z = w$ and $z = -w$, and thus need a more general notion than that of
a super vertex algebra. In this paper we present such a notion: the concept of
a twisted vertex algebra, which generalizes the concept of super vertex
algebra. The two sides of the correspondence of type B constitute two examples
of twisted vertex algebras. The boson-fermion correspondence of type B is thus
an isomorphism between two twisted vertex algebras.
