A new quantization principle from a minimally non time-ordered product

TL;DR

This paper introduces a novel quantization principle based on a minimally non time-ordered product, unifying physical and virtual particles, and providing a new way to construct the physical scattering matrix in quantum field theory.

Contribution

It proposes a new quantization method using a minimally non time-ordered product, linking ghost elimination to purely virtual particles and unitarity preservation.

Findings

The new scattering matrix $S_{ph}$ matches the one from turning ghosts into fakeons.

Classified the most general unitarity-preserving operations via non time-ordered propagators.

Illustrated diagram transformations from simple to complex cases at one and two loops.

Abstract

We formulate a new quantization principle for perturbative quantum field theory, based on a minimally non time-ordered product, and show that it gives the theories of physical particles and purely virtual particles. Given a classical Lagrangian, the quantization proceeds as usual, guided by the time-ordered product, up to the common scattering matrix $S$, which satisfies a unitarity or a pseudounitarity equation. The physical scattering matrix $S_{\text{ph}}$ is built from $S$, by gluing $S$ diagrams together into new diagrams, through non time-ordered propagators. We classify the most general way to gain unitarity by means of such operations, and point out that a special solution "minimizes" the time-ordering violation. We show that the scattering matrix $S_{\text{ph}}$ given by this solution coincides with the one obtained by turning the would-be ghosts (and possibly some would-be physical particles) into purely virtual particles (fakeons). We study tricks to descend and ascend in a unique way among diagrams, and illustrate them in several examples: the ascending chain from the bubble to the hexagon, at one loop; the box with diagonal, at two loops; other diagrams, with more loops.