Generally Covariant Dirac Hamiltonian

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Abstract

The generally covariant Dirac equation reduces to a mathematically simple form with a clear physical meaning that is best demonstrated by the Hamiltonian formalism. The resulting Hamiltonian is compared to the corresponding classical Hamiltonian, and assumes a particularly simple form for the Robertson-Walker metric of the Standard Cosmological Model when that metric is expressed in a coordinate system referred to as Einstein coordinates because it is based on a coordinate constraint recommended by Einstein in his original paper on general relativity. A kinematic definition of distance, based on the form of the classical Hamiltonian, is used in discussing the physical meaning of the results.

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