Trees

TL;DR

This paper introduces an algebraic formalism for quantum field theory that proves a factorization theorem for tree graphs, enabling the integration over internal variables in many space-times.

Contribution

It develops a formalism that provides a complete description of generalized retarded functions for any tree graph in quantum field theory.

Findings

Proves a factorization theorem for tree graphs' retarded functions

Demonstrates integration over internal variables in various space-times

Provides a formalism for analyzing quantum field interactions on trees

Abstract

An algebraic formalism, developped with V. Glaser and R. Stora for the study of the generalized retarded functions of quantum field theory, is used to prove a factorization theorem which provides a complete description of the generalized retarded functions associated with any tree graph. Integrating over the variables associated to internal vertices to obtain the perturbative generalized retarded functions for interacting fields arising from such graphs is shown to be possible for a large category of space-times.