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Relativistic quantum physics with hyperbolic numbers

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2005Embargo end date: 01 Jan 2000 English Publisher:Elsevier BVJournal:Physics Letters B, volume 625, pages 313-323 (issn: 0370-2693, Copyright policy )
Authors: Ulrych, S.;

doi: 10.1016/j.physletb.2005.08.072 , 10.48550/arxiv.physics/0009079

arXiv: physics/0009079

Relativistic quantum physics with hyperbolic numbers

Abstract

A representation of the quadratic Dirac equation and the Maxwell equations in terms of the three-dimensional universal complex Clifford algebra is given. The investigation considers a subset of the full algebra, which is isomorphic to the Baylis algebra. The approach is based on the two Casimir operators of the Poincare group, the mass operator and the spin operator, which is related to the Pauli-Lubanski vector. The extension to spherical symmetries is discussed briefly. The structural difference to the Baylis algebra appears in the shape of the hyperbolic unit, which plays an integral part in this formalism.

17 pages Latex2e

Keywords

High Energy Physics - Theory, Physics - General Physics, General Physics (physics.gen-ph), Covariant wave equations in quantum theory, relativistic quantum mechanics, Maxwell equations, High Energy Physics - Theory (hep-th), FOS: Physical sciences, quadratic Dirac equation, Spinor and twistor methods applied to problems in quantum theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
63
Top 10%
Top 10%
Average
Green
gold