Three-particle fields as a method of description of baryons in the scattering processes

TL;DR

This paper introduces a three-particle bispinor field model to describe baryons and quark interactions, incorporating a novel approach to gauge invariance and confinement within a relativistic framework.

Contribution

It proposes a new three-particle field model on a subset of Minkowski space and a generalized gauge invariance method, advancing the understanding of quark confinement and baryon structure.

Findings

The model achieves a relativistically consistent description of three-quark systems.

A dynamic equation for quark potential energy is derived.

Solutions indicate quark confinement within the model.

Abstract

In this paper we propose a model within which the keeping of quarks inside a proton and the interaction of these quarks with quarks of another hadron can be described simultaneously. The model of a three-particle bispinor field is used for this purpose. Such a field, in comparison with the usual one-particle field, is considered not on Minkowski space, but on a subset of the tensor product of three Minkowski spaces, which is characterized by the equality of time coordinates of three events (subset of simultaneity). Such a subset cannot be distinguished by the Lorentz invariant method. But due to the multiparticle field transformation law in the transition from one inertial system to another one, the dynamic equations for a three-particle field are consistent with the principle of relativity. The interaction between quarks is introduced by requiring a local SUc(3) invariance. But in the paper a more general way to achieve this invariance than the replacement in Lagrangian of ordinary derivatives by covariance is proposed. The applied procedure leads to a two-index tensor of gauge field, both for Lorentz and internal indices. The connection of this field with the bound states of gluons - glueballs is discussed. It is shown that this glueball field can be represented as the sum of two terms: the classical field, which plays the role of the potential energy of quark interaction in the proton, and the field corresponding to quantum fluctuations around the classical field and describes the quark interaction in proton with other hadrons. A dynamic equation is obtained for the field that determines the potential energy of quark interaction. It is shown that this equation has solutions that correspond to the confinement of quarks.