Perturbative Quantum Field Theory via Vertex Algebras

Understand

In this paper, we explain how perturbative quantum field theory can be formulated in terms of (a version of) vertex algebras.

• Our starting point is the Wilson-Zimmermann operator product expansion (OPE).
• Following ideas of a previous paper [arXiv:0802.2198], we consider a consistency (essentially associativity) condition satisfied by the coefficients in this expansion.
• We observe that the information in the OPE coefficients can be repackaged straightforwardly into "vertex operators" and that the consistency condition then has essentially the same form as the key condition in the theory of vertex algebras.