Non-Perturbative Guiding Center and Stochastic Gyrocenter Transformations: Gyro-Phase Is the <i>Kaluza-Klein</i>5<sup>th</sup>Dimension also for Reconciling General Relativity with Quantum Mechanics

• 作者: Claudio Di Troia
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: GUIDING CENTER TRANSFORMATION Gyrocenter TRANSFORMATION KALUZA-KLEIN General Relativity Higher Dimensions STOCHASTIC Quantum Mechanics Schr?dinger Equation Lorentz’s Force Law
• 年，卷（期）: 2018,（4）
• 页码范围: 701-752
• 页数: 52页
• 分类号: O1

摘要

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 Kaluza-Klein model. Electrodynamics 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 Schrödinger equation.