Mathematical Physics

    

Division Algebra Covariant Derivative

Authors: Richard D. Lockyer

The classical definition for the gradient, divergence and curl utilizing the limit as the volume approaches zero, of the ratio of the integral over the enclosing surface divided by the integral over the enclosed volume can be consolidated to form an Ensemble Derivative. This form is constructed initially as a diffeomorphism between two compatible coordinate sets, one representing the intrinsic division algebra basis; u(v) and the other some basis v(u) within which differentiation is defined. The result is the structure for general covariance for division algebra analysis, where covariant differential equations are constructed by full applications of the Ensemble Derivative.

Comments: 11 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]

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[v1] 2022-02-24 19:49:30

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