Dirac-type equations in a gravitational field, with vector wave function

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.

35 pages. Version accepted for publication in Foundations of Physics. Title changed. Introduction expanded: detailed discussion of i) the vector Dirac wave function and ii) the status of the equivalence principle, main section (Sect. 2) improved by introducing the specific connection earlier (see Theorem 1), and other improvements accounting for the referees' remarks

References in corpus (11)

• Spin, gravity, and inertia
• Prequantum classical statistical model with infinite dimensional phase-space
• Quantum motion of a neutron in a wave-guide in the gravitational field
• Normal frames for non-Riemannian connections
• On bound states of Dirac particles in gravitational fields
• Space isotropy and weak equivalence principle in a scalar theory of gravity
• Normal frames and the validity of the equivalence principle. I. Cases in a neighborhood and at a point
• Dirac equation: Representation independence and tensor transformation
• Dirac equation from the Hamiltonian and the case with a gravitational field
• Hestenes' Tetrad and Spin Connections
• Gravitational effects on light rays and binary pulsar energy loss in a scalar theory of gravity

Cited by in corpus (9)

• Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations
• A non-uniqueness problem of the Dirac theory in a curved spacetime
• A solution of the non-uniqueness problem of the Dirac Hamiltonian and energy operators
• A simpler solution of the non-uniqueness problem of the covariant Dirac theory
• Four-vector vs. four-scalar representation of the Dirac wave function
• Compatibility of symmetric quantization with general covariance in the Dirac equation and spin connections
• Representations of the Dirac wave function in a curved spacetime
• Noether's second theorem in teleparallel gravity
• Non-uniqueness of the Dirac theory in a curved spacetime