Regularization by Test Function
Abstract
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by properties of test functions, in a way that preserves Poincar\'e invariance, microcausality, and the Fock-Hilbert space structure of the free field. The construction can be taken to be a physically comprehensible regularization because we can introduce a sequence that has a limit that is a conventional interacting quantum field, with the usual informal dependence of the effective dynamics on properties of the experimental apparatus made formally explicit as a dependence on the test functions that are used to model the experimental apparatus.
Cite
@article{arxiv.1406.5742,
title = {Regularization by Test Function},
author = {Peter Morgan},
journal= {arXiv preprint arXiv:1406.5742},
year = {2014}
}
Comments
7 pages. Some text adapted from arXiv:1211.2831v2 [math-ph]