Jacobi identity for vertex algebras in higher dimensions

Vertex algebras in higher dimensions, introduced previously by Nikolov, provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra. (c) 2006 American Institute of Physics.