Non-perturbative guiding center and stochastic gyrocenter transformations: gyro-phase is the Kaluza-Klein 5^th dimension also for reconciling General Relativity with Quantum Mechanics

TL;DR

This paper extends guiding center theory to relativistic and gravitational contexts, introduces a Kaluza-Klein interpretation of gyro-phase, and connects gyrocenter dynamics with quantum mechanics through stochastic electromagnetic fluctuations.

Contribution

It presents a non-perturbative, covariant extension of guiding center transformations incorporating gravity and electromagnetic fluctuations, linking gyrokinetics with quantum mechanics.

Findings

Gyro-phase acts as a fifth dimension in Kaluza-Klein theory.

Conservation of magnetic moment remains exact in relativistic regimes.

Gyrocenter motion obeys the Schrödinger equation under stochastic electromagnetic fluctuations.

Abstract

The non perturbative guiding center transformation is extended to the relativistic regime and takes into account electromagnetic fluctuations. The main solutions are obtained in covariant form: the gyrating particle and the guiding particle solutions, both in gyro-kinetic as in MHD orderings. Moreover, the presence of a gravitational field is also considered. The way to introduce the gravitational field is original and based on the Einstein conjecture on the feasibility to extend the general relativity theory to include electromagnetism by geometry, if applied to the extended phase space. In gyro-kinetic theory, some interesting novelties appear in a natural way, such as the exactness of the conservation of a magnetic moment, or the fact that the gyro-phase is treated as the non observable fifth dimension of the \emph{Kaluza-Klein} model. Electrodynamic becomes non local, without the inconsistency of self-energy. Finally, the gyrocenter transformation is considered in the presence of stochastic e.m. fluctuations for explaining quantum behaviors via Nelson's approach. The gyrocenter law of motion is the \emph{Schr\"odinger} equation.