A source fragmentation approach to interacting quantum field theory

• URL: http://arxiv.org/abs/2109.04412v2
• Date: Mon, 13 Feb 2023 18:36:37 GMT
• Title: A source fragmentation approach to interacting quantum field theory
• Authors: Peter Morgan
• Abstract summary: We prove that the time-ordered Vacuum Expectation Values and the S-matrix of a regularized Lagrangian quantum theory can be approximated by a local operator. For the Wightman axioms, this suggests a modification that takes the algebra of measurement operators not to be generated by an operator-valued distribution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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