Introduction to
Vacuum Gauge Electrodynamics

# Overview:

​​​​ The theory of the classical electron can be re-formulated based on a simple application of the causality principle.  Causality is the generator of the vacuum gauge---a powerful theory of potentials well suited to resolve fundamental difficulties associated with classical electron theory, including particle stability and infinite self-energy.

​In the vacuum gauge the potentials become physically meaningful quantities which dilate the vacuum in the near neighborhood of the charge to maintain particle stability at the classical electron radius.

​In addition to particle stability, vacuum dilatation also propagates momentum through the velocity fields of the particle.   This is canonical momentum in the electromagnetic field which moves at the speed of light and has energy  related to its momentum given by the simple formula .

E=pc/2

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## The Maxwell Limit

​​This  document is the basis for the entire theory of the classical electron when the fields are governed by the causality principle.  The essential difference with conventional theory is the requirement  to address the velocity and acceleration fields as independent theories.  The mathematics allows for this by generating vacuum gauge potentials which propagate from the retarded position of the charge.

## The Radius of the Electron

Beginning with the conventional Maxwell-Lorentz theory, a Lagrangian density for the classical electron can be easily constructed based on independent theories of velocity and acceleration fields.

The conventional theory is then completely abandoned in favor of a highly specialized vacuum Lagrangian formulation.  In the new formulation all gauge invariant quantities of the classical theory are still valid except that they are written exclusively in terms of vacuum gauge potentials.

​The merit of using vacuum gauge potentials lies in their ability to solve problems associated with classical electron theory  which cannot be addressed by the conventional theory---Most notably, particle stability and infinite self--energy .

​By far, the most striking feature of the theory is the omni-presence of radiated vacuum energy , even while its inclusion requires such an insignificant amount of mathematics.

## Vacuum Dilatation Functions

​​​​​A theory of Dilatation functions follows by separating out the classical electron charge density from the vacuum Lagrangian.  The resulting theory exists in three spatial dimensions and may still be written as a sum over Fourier Amplitudes.

## Vacuum Gauge Electron in the Spherical Basis

​​Classical electron theory is re-written in a spherically-based coordinate system.  The four-space coordinate transformation is a flat space operation which, nevertheless, requires ten independent Christoffel symbols for its implementation.  All gauge invariant quantities of the classical electron can be represented in the spherically-based system and the stability problem is easily solved.

The spherically based system is well suited to the calculation of a host of integrals, including a second rank total energy tensor.  The divergence theorem may also be applied over the causal light cone.

## ​​The New Radiation Reaction Force

​​ The spherical four-coordinate system is re-introduced and applied to more complicated problems involving particle accelerations.

​The radiation-based theory casts the problem of the radiation reaction into a completely different light.  Reasonable solutions are generated for straight line and circular motion without the difficulties brought about by the conventional theory.

## Multipole Fields in the Vacuum Gauge

​​​Taylor expansions of vacuum gauge potentials are used to perform calculations in the far field limit involving either a single electron near the origin of a coordinate system, or a large collection of N electrons.  The simplicity of the calculations are impressive and stem from the fact that velocity and acceleration fields derive from independent theories.

## Vacuum Energy and the Quantized Electron

​​This document shows several different ways  to quantize the vacuum gauge electron.   The essential strategy is to trade out the gauge field for Dirac gamma matrices which will re-produce all of Dirac electron theory.   An attempt is made to quantize the radiation field required by vacuum gauge electrodynamics.  We're not sure if this is correct or not.  The last section is a (largely speculative) discussion of a cosmological model of the universe with vacuum energy.