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Geometrizing Relativistic Quantum Mechanics

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Abstract

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of them in the non-relativistic limit.

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Authors and Affiliations

  1. Instituto de Cosmologia Relatividade Astrofisica ICRA—CBPF, Rua Dr. Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro, Brazil

    F. T. Falciano, M. Novello & J. M. Salim

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  1. F. T. Falciano
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  2. M. Novello
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  3. J. M. Salim
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Correspondence to F. T. Falciano.

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Falciano, F.T., Novello, M. & Salim, J.M. Geometrizing Relativistic Quantum Mechanics. Found Phys 40, 1885–1901 (2010). https://doi.org/10.1007/s10701-010-9496-1

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  • DOI: https://doi.org/10.1007/s10701-010-9496-1

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