Gauge invariant formulation of the self-interacting Duffin-Kemmer-Petiau equations

TL;DR

This paper presents a gauge invariant formulation of the self-interacting Duffin-Kemmer-Petiau equations by expressing the gauge potential and field strength tensor in terms of matter field bilinear currents, extending the algebraic structure analysis.

Contribution

It introduces a novel gauge invariant approach to self-interacting DKP equations, expressing gauge fields as functions of matter currents, with detailed algebraic structure analysis.

Findings

Derived a rational expression for gauge potential in terms of matter currents.

Established algebraic structure of bilinear currents for the 5-component DKP system.

Provided a gauge invariant formulation analogous to the Dirac equation case.

Abstract

We show that the Duffin-Kemmer-Petiau equation, minimally coupled to an Abelian gauge field, can be regarded as a matrix equation for the gauge potential produced internally from the matter fields. This can be solved as a rational expression in terms of currents bilinear in the matter wavefunction, together with a similar expression for the field strength tensor, thus providing a gauge invariant formulation of the self-interacting DKP equations. We give the derivation of this result for the 5 component DKP system, by analogy with the Dirac equation case. To this end, we establish the algebraic structure of the set of bilinear currents, and the properties of the minimal generating set, which consists of two scalars and two four-vectors, together with a single quadratic constraint.