J. A. Rizcalla | Searcharxiv

arXiv1998

Algebrodynamical Approach in Field Theory: Bisingular Solution and its Modifications

The criterion of differentiability of functions of quaternion variable is used as the basis of some algebraic field theory. Its necessary consequences are free Maxwell and Yang-Mills equations. The differentiability equations may be integrated in twistor variables and are reduced to algebraic ones. In the article we present bisingular solution and its topological modifications. Related EM-fields appear to be just the well-known Born solution and its modifications with singular structure of ring-like and toroidal topology. General problems of the algebrodynamical approach are discussed.

gr-qc↗

arXiv1998

Particles as singularities within the unified algebraic field dynamics

We consider a nonlinear generalization of Cauchy-Riemann eqs. to the algebra of biquaternions. From here we come to "universal generating equations" (1) which deal with 2-spinor and gauge fields and form the basis of some unified algebraic field theory. For each solution of eqs.(1) the components of spinor field satisfy the eikonal and d'Alembert eqs., and the strengths of gauge field - both Maxwell and Yang-Mills eqs. We reduce eqs.(1) to that of shear-free geodesic null congruence and integrate them in twistor variables. Particles are treated as concurrent singularities of the effective metric and the electromagnetic field. For unisingular solutions the electric charge is quantized, and the metric is of Schwarzschild or Kerr type. Bisingular solutions are announced too.

gr-qc↗