Journal ArticleDOI
Real spinor fields.
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In this paper, a geometrical interpretation for the (−1)½ which appears explicitly in the Dirac equation is presented. But it does not support the spinor theory.Abstract:
The Dirac equation is expressed entirely in terms of geometrical quantities by providing a geometrical interpretation for the (−1)½ which appears explicitly in the Dirac equation. In the modification of the Dirac electron theory which ensues, the (−1)½ appears as the generator of rotations in the spacelike plane orthogonal to the plane containing the electron current and spin vectors. This amounts to a further ``relativistic'' constraint on the spinor theory and so may be expected to have physical consequences. It does not, however, conflict with well‐substantiated features of the Dirac theory.read more
Citations
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The zitterbewegung interpretation of quantum mechanics
TL;DR: In this article, a reformulation of the Dirac theory shows that thezitterbewegung need not be attributed to interference between positive and negative energy states as originally proposed by Schroedinger.
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Oersted Medal Lecture 2002: Reforming the mathematical language of physics
TL;DR: Geometric algebra as discussed by the authors is a unified mathematical language for the whole of physics that facilitates learning and enhances physical insight, with emphasis on how it simplifies and integrates classical and quantum physics and introduces research-based reform into a conservative physics curriculum is a challenge for the emerging PER community.
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Spacetime physics with geometric algebra
TL;DR: Spatio-Time Algebra (STA) as discussed by the authors is a unified mathematical language for physics that simplifies, extends, and integrates the mathematical methods of classical, relativistic, and quantum physics while elucidating geometric structure of the theory.
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Observables, operators, and complex numbers in the Dirac theory
TL;DR: In this article, the geometrical formulation of the Dirac theory with spacetime algebra is shown to be equivalent to the usual matrix formalism, and some basic relations among local observables in the nonrelativistic limit are determined.
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ELKO, flagpole and flag-dipole spinor fields, and the instanton Hopf fibration
TL;DR: In this paper, it was shown that the instanton Hopf fibration map (S^3...S^7\to S^4) prevents ELKO to describe an instanton, giving a suitable physical interpretation to ELKO.
References
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Journal ArticleDOI
The quantum theory of the electron
TL;DR: In this article, it was shown that the incompleteness of the previous theories lying in their disagreement with relativity or, alternatetically, with the general transformation theory of quantum mechanics leads to an explanation of all duplexity phenomena.
Book
Space-time algebra
TL;DR: In this paper, the second edition of the Second Edition of Geometric Algebra, the authors present an approach to the interpretation of Clifford Algebra and the structure of Clifford algebras.