Regular charged formation on an arbitrary worldline in a space with torsion

2016

Gravit. Cosmol.

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We consider a manifestly Lorentz invariant form L of the biquaternion algebra and its generalization to the case of curved manifold. The conditions of L-differentiability of L-functions are formulated and considered as the primary equations for fundamental fields modeled with such functions. The exact form of the effective affine connection induced by L-differentiability equations is obtained for the flat and curved cases. In the flat case, the integrability conditions of the latter leads to the self-duality of the corresponding curvature, thus ensuring that the source-free Maxwell and SL(2, C) Yang-Mills equations hold on the solutions of the L-differentiability equations.

Section: Analysis and Induced Field Dynamics On The Relativistic Alge...mentioning

confidence: 99%

“…Let us now return to the integrability conditions (10). Since the spinor ξ(x) is not arbitrary, the curvature R is not null.…”

Section: Analysis and Induced Field Dynamics On The Relativistic Alge...mentioning

confidence: 99%

Relativistic algebra of space-time and algebrodynamics

2016

Gravit. Cosmol.

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“…Unlike the potentials A µ , the components K µ of the CCVF are evidently defined up to a multiplicative constant. It is noteworthy that equations (16), (17) and (20) are reparametrization invariant, though, unlike the situation in Weyl geometry [10], the 4potentials (20) do not transform gradient-wise under the transformation τ → σ(τ ), so the reparametrization group is not explicitly related to the electromagnetic gauge group. [10].…”

Section: The Fundamental Solutionmentioning

confidence: 99%

“…As mentioned earlier, in this case we regard the second pair of Maxwell's equations as the definition of the current and charge densities. In the stationary case, the simplest spherically symmetric solution can easily be found [17]…”

Section: The Fundamental Solutionmentioning

confidence: 99%

“…Nevertheless, despite its mathematical elegance, it is well known that Weyl's unified theory, in its classical form, encounters major interpretation difficulties, related primarily to the change of scale upon parallel transport [5,11,12]. Since the origin of most of these difficulties can be traced back to the geometry's nonmetricity, in the present paper we attempt a CCVF in a different kind of geometry -the so-called Norden geometry [13] -which is metric compatible, possesses conformal curvature and allows a natural EM interpretation through the trace of the torsion tensor [15,17].…”

Section: Introductionmentioning

confidence: 99%

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Regularized Lienard-Wiechert fields in a space with torsion

2015

Gravit. Cosmol.

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A natural modification of the equations of covariantly-constant vector fields (CCVF) in Weyl geometry leads us to consider a metric compatible geometry possessing conformal curvature and torsion fully determined by its trace. The latter is interpreted as a form of the electromagnetic (EM) 4-potentials and, on a fixed metric background, turns out to be fully determined by the CCVF equations. When the metric is set Minkowskian, the named equations possess two topologically distinct solutions, with the associated EM fields being asymptotically of the Lienard-Wiechert type and having distributed sources, with a fixed ("elementary") value of the electric charge. One of the solutions is everywhere regular, whereas the other -singular on a 2-dimensional shell. The speed of propagation of EM fields depends on the local charge density and only asymptotically approaches the speed of light.

Maxwell, Yang–Mills, Weyl and eikonal fields defined by any null shear-free congruence

Int. J. Geom. Methods Mod. Phys.

2017

We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, C) Yang-Mills and complex Maxwell fields, the latter produced by integervalued electric charges ("elementary" for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding "particle-like" field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit non-trivial collective dynamics simulating physical interactions.