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Dirac Theory in Hydrodynamic Form

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Abstract

We consider quantum mechanics written in hydrodynamic formulation for the case of relativistic spinor fields to study their velocity: within such a hydrodynamic formulation it is possible to see that the velocity as is usually defined can not actually represent the tangent vector to the trajectories of particles. We propose an alternative definition for this tangent vector and hence for the trajectories of particles, which we believe to be new and the only one possible. We discuss how these results are a necessary step to take in order to face further problems, like the definition of trajectories for multi-particle systems or ensembles, as they happen to be useful in many applications and interpretations of quantum mechanics.

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Authors and Affiliations

  1. DIME, Genoa University, Via all’Opera Pia 15, 16145, Genova, Italy

    Luca Fabbri

  2. INFN, Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy

    Luca Fabbri

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  1. Luca Fabbri
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Luca Fabbri did all computations, wrote the main manuscript and reviewed the final version.

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Correspondence to Luca Fabbri.

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Fabbri, L. Dirac Theory in Hydrodynamic Form. Found Phys 53, 54 (2023). https://doi.org/10.1007/s10701-023-00695-w

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