Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-02-08
Found.Phys.38:1020-1045,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
35 pages. Version accepted for publication in Foundations of Physics. Title changed. Introduction expanded: detailed discussio
Scientific paper
10.1007/s10701-008-9249-6
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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