A source fragmentation approach to interacting quantum field theory

TL;DR

This paper introduces a novel approach to interacting quantum field theory using local operator approximations of the S-matrix and vacuum expectation values, emphasizing a source fragmentation method that offers a top-down construction of interactions.

Contribution

It proposes a source fragmentation approach that approximates key quantum field theory quantities with local operators, challenging traditional bottom-up methods.

Findings

Provides a corollary to the Reeh-Schlieder theorem.

Suggests a modification to the Wightman axioms for measurement operators.

Offers a top-down construction of interacting quantum fields.

Abstract

A corollary to the Reeh-Schlieder theorem is proved: that the time-ordered Vacuum Expectation Values and the S-matrix of a regularized Lagrangian quantum theory can be approximated by a local operator that uses nonlinear functionals of a locally supported source function. For the Wightman axioms, this suggests a modification that takes the algebra of measurement operators not to be generated by an operator-valued distribution. The use of operator-valued nonlinear functionals of a source function introduces many abstract fragments of the source to give a well-defined top-down construction of interacting quantum fields, in contrast to a bottom-up blocking and scaling construction or to analyzing response to changing renormalization scales. The construction can also be thought of as solving a localized inverse problem for the interacting dynamics or as a generating function for multi-point bound state fields.