Heiner Olbermann

Perturbative Quantum Field Theory and Vertex Algebras


Recently, a new viewpoint on perturbative QFT has been formulated that focusses on the operator product expansion elevating it to an axiom of the theory. In this talk, we want to point out the similarities of this approach to the theory of vertex algebras. Starting from the vertex algebra of the bosonic Euclidean free field, we propose a set of graphical rules that in principle determine the perturbations of the vertex operators in an interacting theory governed by a nonlinear field equation. The resulting expressions involve special functions of hypergeometric kind, which hints at a deep relation between vertex algebras and the theory of these functions.