We define the 2Zβ-graded meromorphic open-string vertex
algebra that is an appropriate noncommutative generalization of the vertex
operator superalgebra. We also illustrate an example that can be viewed as a
noncommutative generalization of the free fermion vertex operator superalgebra.
The example is bulit upon a universal half-integer-graded non-anti-commutative
Fock space where a creation operator and an annihilation operator satisfy the
fermionic anti-commutativity relation, while no relations exist among the
creation operators. The former feature allows us to define the normal ordering,
while the latter feature allows us to describe interactions among the fermions.
With respect to the normal ordering, Wick's theorem holds and leads to a proof
of weak associativity and a closed formula of correlation functions.Comment: 37 pages. Comments and suggestions are welcome