Nondynamical modeling of resonances in a Quantum Field formalism

TL;DR

This paper introduces a non-dynamical, Poincaré invariant approach to modeling quantum field resonances through algebraic deformations, avoiding traditional renormalization complexities.

Contribution

It presents a novel algebraic framework for non-dynamical quantum field deformations that naturally incorporate resonance and scaling properties without requiring dynamical interactions.

Findings

Constructed energy and momentum operators post hoc from algebraic deformations.

Introduced 'convex hull microcausality' as a weakened causality condition.

Enabled the construction of interacting quantum fields within this framework.

Abstract

Well-defined nonlinear deformations of free quantum fields are introduced as manifestly Poincar\'e invariant scaling and resonance properties of non-dynamical scale models in Minkowski space, instead of introducing nonlinear dynamical deformations of free quantum fields that require the various truncations and scaling corrections of regularization and renormalization. With the given algebraic construction, energy and momentum operators can be constructed \emph{ex post facto} as the generators of translations. A weakened version of microcausality emerges naturally, "convex hull microcausality" ---that operators associated with two regions of space--time must commute if \emph{the convex hulls of} those regions are space-like separated---, which is enough for us to be able to construct an abundant class of interacting quantum fields.