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Dirac-Type Equations in a Gravitational Field, with Vector Wave Function

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Abstract

An analysis of the classical-quantum correspondence shows that it needs to identify a preferred class of coordinate systems, which defines a torsionless connection. One such class is that of the locally-geodesic systems, corresponding to the Levi-Civita connection. Another class, thus another connection, emerges if a preferred reference frame is available. From the classical Hamiltonian that rules geodesic motion, the correspondence yields two distinct Klein-Gordon equations and two distinct Dirac-type equations in a general metric, depending on the connection used. Each of these two equations is generally-covariant, transforms the wave function as a four-vector, and differs from the Fock-Weyl gravitational Dirac equation (DFW equation). One obeys the equivalence principle in an often-accepted sense, whereas the DFW equation obeys that principle only in an extended sense.

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  1. Laboratory “Soils, Solids, Structures—Risks”, CNRS & University of Grenoble, Grenoble, France

    Mayeul Arminjon

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Correspondence to Mayeul Arminjon.

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Part of this work was done while the author was at Dipartimento di Fisica, Università di Bari and INFN Bari, Italy.

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Arminjon, M. Dirac-Type Equations in a Gravitational Field, with Vector Wave Function. Found Phys 38, 1020–1045 (2008). https://doi.org/10.1007/s10701-008-9249-6

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