## A Generalized Klein Gordon Equation with a Closed System Condition for the Dirac-Current Probability/field Tensor

**Authors:** E.P.J. de Haas

I begin with a short historical analysis of the problem of the electron from Lorentz to Dirac. It is my opinion that this problem has been quasi frozen in time because it has always been formulated within the paradigm of the Minkowski-Laue consensus, the relativistic version of the Maxwell-Lorentz theory. By taking spin away from particles and putting it in the metric, thus following Dirac's vision, I start my attempt to formulate an alternative math-phys language. In the created non-commutative math-phys environment, biquaternion and Clifford algebra related, I formulate an alternative for the Minkowski-Laue consensus. This math-phys environment allows me to formulate a generalization of the Dirac current into a Dirac probability/field tensor with connected closed system condition. This closed system condition includes the Dirac current continuity equation as its time-like part. A generalized Klein Gordon equation that includes this Dirac current probability tensor is formulated and analyzed. The Standard Model's Dirac current based Lagrangians are generalized using this Dirac probability/field tensor. The Lorentz invariance or covariance of the generalized equations and Lagrangians is proven. It is indicated that the Dirac probability/field tensor and its closed system condition closes the gap with General Relativity quite a bit.

**Comments:** 70 Pages.

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### Submission history

[v1] 2018-10-12 15:23:41

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