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 wave function, 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.

Item Type:	Refereed Article
Keywords:	Duffin–Kemmer–Petiau equations, Duffin–Kemmer–Petiau algebra, Maxwell equations, self-interacting system, relativistic wave equation
Research Division:	Physical Sciences
Research Group:	Particle and high energy physics
Research Field:	Particle physics
Objective Division:	Expanding Knowledge
Objective Group:	Expanding knowledge
Objective Field:	Expanding knowledge in the mathematical sciences
UTAS Author:	Jarvis, PD (Dr Peter Jarvis)
UTAS Author:	Inglis, SM (Mr Shaun Inglis)
ID Code:	151614
Year Published:	2022
Deposited By:	Mathematics
Deposited On:	2022-08-02
Last Modified:	2023-01-10
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