Algbrodynamics over complex space and phase extension of the Minkowski geometry

Abstract

First principles should predetermine physical geometry and dynamics both together. In the "algebrodynamics" they follow solely from the properties of the biquaternion algebra $\B$ and the analysis over $\B$. We briefly present the algebrodynamics on the Minkowski background based on a nonlinear generalization to $\B$ of the Cauchi-Riemann analyticity conditions. Further, we consider the effective real geometry uniquely resulting from the structure of multiplication in $\B$ which turns out to be of the Minkowski type, with an additional phase invariant. Then we pass to study the primordial dynamics that takes place in the complex $\B$ space and brings into consideration a number of remarkable structures: an ensemble of identical correlated matter pre-elements ("duplicons"), caustic-like signals (interaction carriers), a concept of random complex time resulting in irreversibility of physical time at a macrolevel, etc. In partucular, the concept of "dimerous electron" naturally arises in the framework of complex algebrodynamics and, together with the above-mentioned phase invariant, allows for a novel approach to explanation of quantum interference phenomena alternative to the recently accepted paradigm of wave-particle dualism.

14 pages, twocolumn

References in corpus (7)

• The Universe of Fluctuations
• Lorentz symmetry violation without violation of relativistic symmetry
• Complex Kerr Geometry and Nonstationary Kerr Solutions
• Maxwell Fields and Shear-Free Null Geodesic Congruences
• Biquaternion Electrodynamics and Weyl-Cartan Geometry of Space-Time
• Electromagnetic Dipole Radiation Fields, Shear-Free Congruences and Complex Center of Charge World Lines
• Effective connections and fields associated with shear-free null congruences

Cited by in corpus (9)

• Collective Lorentz invariant dynamics on a single "polynomial" worldline
• Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence
• The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts
• Algebraic roots of Newtonian mechanics: correlated dynamics of particles on a unique worldline
• Relativistic Algebra of Space-Time and Algebrodynamics
• Three kinds of particles on a single rationally parameterized worldline
• Algebraic dynamics on a single worldline: Vieta formulas and conservation laws
• Self-Dual Connections and the Equations of Fundamental Fields in a Weyl-Cartan Space
• The algebrodynamics: super-conservative collective dynamics on a "Unique Worldline'' and the Hubble's law