Non-Trivial Effects of Sourceless Forces for Spinors: Toward an Aharonov-Bohm gravitational effect?
arXiv:1909.01733 · doi:10.1140/epjc/s10052-019-7380-5
Abstract
Spinor fields are written in polar form so as to compute their tensorial connection, an object that contains the same information of the connection but which is also proven to be a real tensor. From this, one can still compute the Riemann curvature, encoding the information about gravity. But even in absence of gravity, when the Riemann curvature vanishes, it may still be possible that the tensorial connection remains different from zero, and this can have effects on matter. This is shown with examples in the two known integrable cases: the hydrogen atom and the harmonic oscillator. The fact that a spinor can feel effects due to sourceless actions is already known in electrodynamics as the Aharonov-Bohm phenomenon. A parallel between the electrodynamics case and the situation encountered here will be drawn. Some ideas about relativistic effects and their role for general treatments of quantum field theories are also underlined.
arXiv comment10 pages
References in corpus (11)
- ELKO, flagpole and flag-dipole spinor fields, and the instanton Hopf fibration
- Classification of Singular Spinor Fields and Other Mass Dimension One Fermions
- Unfolding Physics from the Algebraic Classification of Spinor Fields
- Bilinear Covariants and Spinor Fields Duality in Quantum Clifford Algebras
- Revealing how different spinors can be: the Lounesto spinor classification
- Questing for Algebraic Mass Dimension One Spinor Fields
- A generally-relativistic gauge classification of the Dirac fields
- Torsion Gravity for Dirac Fields
- Covariant Inertial Forces for Spinors
- General Dynamics of Spinors
- Geometry, Zitterbewegung, Quantization
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