1207.3791 (Ricardo Gallego Torromé)

Geometry of generalized higher order fields. Applications to classical
linear electrodynamics    [PDF]

Ricardo Gallego Torromé

Motivated by the problem of radiation reaction in linear classical electrodynamics, a theory of {\it generalized higher order tensor and differential forms} is introduced. We discuss a cohomology and integration theory for generalized higher order forms. Then we pay attention to a special type of generalized higher order field associated with {\it bounded maximal proper acceleration}. Using such theory of generalized higher order fields, a generalization of the Maxwell-Lorentz theory with fields living on higher order jet bundles is described. The theory is free of the pathologies of the standard linear classical linear electrodynamics. The theory is not local in the usual sense, since fields live on higher jet bundles over the spacetime. Combining the generalized higher order electrodynamics with {\it maximal acceleration geometry}, we show that the evolution of a point charged particle interacting with generalized higher order fields is described by solutions of a second order ordinary differential equation. Such equation is Lorentz invariant, causal, and compatible with Newton's first law and the energy-momentum conservation. In addition, it is free of run-away solutions and pre-accelerated solutions of the Dirac's type. In the final section we comment on the assumptions and on related developments of the theory presented in this work.

View original: http://arxiv.org/abs/1207.3791