QJT as a Regularization: Origin of the New Gauge Anomalies

TL;DR

This paper explores how regularizing quantum field theory with finite p-jets leads to new gauge anomalies that diverge upon removing the regulator, but can be controlled in four dimensions with specific field content.

Contribution

It introduces a novel gauge anomaly arising from jet regularization of QFT, highlighting its divergence and conditions for finiteness in four-dimensional spacetime.

Findings

New gauge anomalies are identified in jet-regularized QFT.

Anomalies diverge as the regulator is removed, but can be finite in 4D with specific fields.

Unphysical fields violating spin-statistics are involved in anomaly cancellation.

Abstract

QJT is considered as a regularization of QFT, where the fields are replaced by finite $p$-jets. The regularized phase space is infinite-dimensional, because not all histories are determined by initial conditions. Gauge symmetries are not fully preserved by the regularization, and gauge anomalies arise. These anomalies are of a new type, not present in QFT. They generically diverge when the regulator is removed, but can be made finite with a particular choice of field content, provided that spacetime has at most four dimensions. The field content appears to include unphysical fields that violate the spin-statistics theorem.