Double gauge invariance and covariantly-constant vector fields in Weyl geometry

Int. J. Geom. Methods Mod. Phys.

2017

Self Cite

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.

Section: The Eikonal Equation and General Solution To The Generating mentioning

confidence: 92%

Section: The Eikonal Equation and General Solution To The Generating mentioning

confidence: 99%

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

Int. J. Geom. Methods Mod. Phys.

2017

Self Cite

“…The associated non-metricity vector A µ gives then rise to the well-known Lienard-Wiechert (LW) solution in classical electrodynamics, with the electric charge being naturally fixed in value to ±1. As it turns out [10], for the fundamental solution the above mentioned additional symmetry is closely related to the reparametrization group of the point charge's worldline. On the other hand, the charge "self-quantization" can be traced to the universality of the speed of light, with its sign being associated with the retarded/advanced LW anzatz, hence with the direction of the "arrow of time", in close analogy with Feynman's well-known representation.…”

Section: Introductionmentioning

confidence: 99%

“…By contrast, in Weyl geometry [1,9], when (the conformal class of) the metric is fixed, the existence of a CCVF imposes stringent restrictions on the nonmetricity vector A µ identified traditionally with the electromagnetic (EM) potentials. In this case, the system of CCVF equations (and its fundamental solution) possess an array of remarkable properties [10]. In particular, in addition to the classical invariance w.r.t.…”

Section: Introductionmentioning

confidence: 99%

Regularized Lienard-Wiechert fields in a space with torsion

2015

Gravit. Cosmol.

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.

“…The very GSE equations (in form (2)) can be considered as the equations of covariantly constant fields in the corresponding space with the Weyl-Cartan connection [2], dF = ΩF . Note that covariantly constant fields in Weyl-Cartan affine connection spaces of different types can be generally used for promising geometric interpretations of electromagnetism [5].…”

mentioning

confidence: 99%

Self-dual connections and the equations of fundamental fields in a Weyl–Cartan space

2018

Phys. Part. Nuclei

Spaces with a Weyl-type connection and torsion of a special type induced by the structure of the differentiability conditions in the algebra of complex quaternions are considered. The consistency of these conditions implies the self-duality of curvature. The Maxwell and SL(2, C) Yang-Mills fields associated with the irreducible components of the connection also turn out to be self-dual, so that the corresponding equations are fulfilled on the solutions of the generating system. Using the twistor structure of the latter, its general solution is obtained. The singular locus has a string-like (particle-like) structure and generates the self-consistent algebraic dynamics of the string system.