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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