Theory

• Introduction to Wave Electricity
• The Hidden Geometry of the Hyperbolic Unit
• The origin of the Lorentz factor from an infinite idempotent splitting
• From the geometric state of the electron to the orbit of the hydrogen atom
• Mass as a geometric projection of a closed wave. Why is the mass of a photon zero?
• A Unified Geometric Model of Wave and Particle Motion
• Geometric origin of the square of the fine structure constant and the parameters of the Bohr atom
• Anomalous magnetic moment of the electron

Lorentz factor and split geometry

• The origin of the Lorentz factor from an infinite idempotent splitting
• Geometric origin of the Lorentz factor and the energy invariant

Electron and positron spin, polarization

• Electron spin as a consequence of the double orbital cycle in the geometric model
• Transition of electron and positron spin into photon polarization
• Multilevel idempotent splitting of the electron: the origin of spin 1/2 and the transition to a photon

Geometric construction of the orbits of the hydrogen atom

• 1. First orbit
• 2. Higher Orbits and Subtle Splitting
• Geometric Origin of the Generalized Rydberg Law

Diffraction of particles by a slit as a manifestation of the spatial phase of the operator J

• 1. Passing through one slit
• 2. Passing through two slits

Heisenberg uncertainty, related phases

• The uncertainty of the internal phase as a geometric basis for the Heisenberg principle
• Associated random phases. From particle uncertainty to two-particle interference

Geometric model of the internal structure of an electron

• 1. From an Idempotent Basis to a Geometric Model of the Electron’s Internal Structure
• 2. Double inner orbit of the electron, spinor periodicity and magnetic precession

A new Cartesian basis of two independent complex planes

• 1. A new Cartesian basis
• 2. Movement through Complex Modulation of a Cartesian Basis
• 3. Internal motion of the electron and the origin of its magnetic moment
• 4. Schrödinger equation in split operator geometry

Temporal field and its projections

• 1. The temporal field and the origin of space
• 2. Temporal Field Projections. Origin of Electric, Magnetic, and Wave Fields

Electrodynamics

1. Electrical forces

• Geometric origin of electric force
• Attraction and repulsion of charges and currents as two projections of operator correlation

2. Electromagnetic waves

• Geometric origin of electric and magnetic fields
• Geometrical origin of the propagating wave

Sum and difference of velocities as a composition of Doppler projections

• 1. Same internal state
• 2. Different internal states

The Birth of Matter from Split Operators

• 1. Construction of Known Particles from Normalized Operators
• 2. Operator Classification of Matter

Geometric representation of particle interactions

• 1. States of particles and their transformations in the i-basis
• 2. Geometric rule of particle interaction
• 3. Branches as the basis for particle interaction
• 4. Probabilities and dynamics of branch restructuring

Capacitance and inductance of an electron and a positron

• The geometric meaning of the capacitance and inductance of an electron
• Second magnetic field in an electron
• 2.1 Mathematical Model
• 2.2 Mathematical Model. Completion
• Coefficientless Coulomb's Law and Ampere's Law

Applications

• The fine structure constant as the basis of the logarithmic scale of physical quantities
• Relativistic force as a change in an external parameter
• Appendix: Commutative algebra for a new Cartesian basis
• Dark matter as a scalar potential

Early Works

• Wave Electricity (WEL). Part 1. Introduction
• Wave electricity. Part 2. General form of the law of interactions