Relativity and Cosmology


Disposing Classical Field Theory

Authors: Hans Detlef Hüttenbach

This article is about the concept of mass and electric charge: When the fundamental relativistic equation E^2=m^2 c^4+〖|p|〗^2 c^2 is solved in the complex, this inevitably leads to an irreducible representation of the extended Lorentz group as U(4) operating on the complex Clifford algebra Cl(1,3) in which mass is a complex 4x4-spinor. Spinors are a direct consequence of taking the root of the Minkowski square distance. Doing so with the Minkowski square of differentials then gives a spinor-valued differential form. With that, classical electrodynamics is shown to be extendable into a relativistically invariant theory, in fact the simplest possible relativistically invariant one. Its symmetries reveal a unified concept of classical charge and mass. A dynamical system based on this, splits into the direct sum of a dynamical system of pure electromagnetic charges and one of purely neutral particles. In it, charged particles must be fermionic in order to conserve their net charge, and neutral non-magnetic ones are bosonic in order to be able to assign to them a positive mass. Also, it will be seen that within the Clifford algebra, the Hamiltonian of a self-interacting mechanical dynamical system of particles can be given in a closed form. I end the paper with a section on superconductivity, where it is shown that superconducting material should electromagnetically behave as opaque, dark matter.

Comments: 21 pages

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Submission history

[v1] 2012-09-10 11:52:58

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