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Parallel Objects and Field Equations

Stoil Donev·Maria Tashkova
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Abstract

This paper considers a generalization of the existing concept of parallel (with respect to a given connection) geometric objects and its possible usage as a suggesting rule in searching for adequate field equations in theoretical physics. The generalization tries to represent mathematically the two-sided nature of the physical objects, the {\it change} and the {\it conservation}. The physical objects are presented mathematically by sections $Ψ$ of vector bundles, the admissible changes $DΨ$ are described as a rsult of the action of appropriate differential operators $D$ on these sections, and the conservation propertieis are accounted for by the requirement that suitable projections of $DΨ$ on $Ψ$ and on other appropriate sections must be zero. It is shown that the most important equations of theoretical physics obey this rule. Extended forms of Maxwell and Yang-Mills equations are also considered.

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Stoil Donev, Maria Tashkova. 2002-05-30. Parallel Objects and Field Equations. https://arxiv.org/abs/math-ph/0205046

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