Regularization by Test Function

TL;DR

This paper introduces a novel regularization method for quantum fields by modifying their effective dynamics through test functions, maintaining key physical principles and explicitly modeling experimental apparatus effects.

Contribution

It presents a new approach to regularizing quantum fields by nonlinear test function dependence, preserving fundamental symmetries and providing a physically interpretable framework.

Findings

Constructs a sequence of test function modifications with a well-defined limit.

Maintains Poincaré invariance, microcausality, and Fock-Hilbert space structure.

Explicitly models the dependence of quantum field dynamics on experimental apparatus.

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.