Charged and Electromagnetic Fields from Relativistic Quantum Geometry

Marcos Arcodía,Mauricio Bellini

doi:10.3390/universe2020013

Abstract

In the recently introduced Relativistic Quantum Geometry (RQG) formalism, the possibility was explored that the variation of the tensor metric can be done in a Weylian integrable manifold using a geometric displacement, from a Riemannian to a Weylian integrable manifold, described by the dynamics of an auxiliary geometrical scalar field θ, in order that the Einstein tensor (and the Einstein equations) can be represented on a Weyl-like manifold. In this framework we study jointly the dynamics of electromagnetic fields produced by quantum complex vector fields, which describes charges without charges. We demonstrate that complex fields act as a source of tetra-vector fields which describe an extended Maxwell dynamics.

Highlights

The consequences of non-trivial topology for the laws of physics has been a topic of perennial interest for theoretical physicists [1], with applications to non-trivial spatial topologies [2] like Einstein-Rosen bridges, wormholes, non-orientable spacetimes, and quantum-mechanical entanglements
Geometrodynamics [3,4] is a picture of general relativity that studies the evolution of the spacetime geometry
The key notion of the Geometrodynamics was the idea of charge without charge

Summary

Introduction

The consequences of non-trivial topology for the laws of physics has been a topic of perennial interest for theoretical physicists [1], with applications to non-trivial spatial topologies [2] like Einstein-Rosen bridges, wormholes, non-orientable spacetimes, and quantum-mechanical entanglements. With the construction of ungauged supergravity theories it was realised that the Abelian gauge fields in such theories were source-free, and so the charges arising therein were central charges [5] and as consequence satisfied a BPS bound [6] where the embedding of Einstein-Maxwell theory into N = 2 supergravity theory was used. An important fact is that the Einstein tensor complies with the gauge-invariant transformations studied in a previous work [12]. This method is very useful because can be used to describe, for instance, nonperturbative back-reaction effects during inflation [13].

RQG Revisited

Gauge-Invariance and Quantum Dynamics

Charged Geometry and Vector Field Dynamics

Dynamics of the Complex Fields

Final Remarks