Purely virtual extension of quantum field theory for gauge invariant fields: Yang-Mills theory

TL;DR

This paper introduces a purely virtual extension to quantum gauge theories, enabling gauge-invariant off-shell correlation functions without affecting physical S-matrix elements, ensuring renormalizability and unitarity.

Contribution

It develops a novel purely virtual cloud sector in quantum field theory that preserves gauge invariance and unitarity while allowing off-shell gauge-invariant correlation functions.

Findings

One-loop two-point functions are gauge and cloud independent.

Absorptive parts of dressed propagators are positive and physical.

The theory remains renormalizable and unitary with the extension.

Abstract

We extend quantum field theory by including purely virtual "cloud" sectors, to define physical off-shell correlation functions of gauge invariant quark and gluon fields, without affecting the $S$ matrix amplitudes. The extension is made of certain cloud bosons, plus their anticommuting partners. Both are quantized as purely virtual, to ensure that they do not propagate ghosts. The extended theory is renormalizable and unitary. In particular, the off-shell, diagrammatic version of the optical theorem holds. We calculate the one-loop two-point functions of dressed quarks and gluons, and show that their absorptive parts are gauge independent, cloud independent and positive (while they are generically unphysical if the cloud sectors are not purely virtual). A gauge/cloud duality simplifies the computations and shows that the gauge choice is just a particular cloud. It is possible to dress every field insertion with a different cloud. We compare the purely virtual extension to previous approaches to similar problems.