A solution of the non-uniqueness problem of the Dirac Hamiltonian and energy operators

Abstract

In a general spacetime, the possible choices for the field of orthonormal tetrads lead (in standard conditions) to equivalent Dirac equations. However, the Hamiltonian operator is got from rewriting the Dirac equation in a form adapted to a particular reference frame, or class of coordinate systems. That rewriting does not commute with changing the tetrad field $(u_{\alpha })$. The data of a reference frame F fixes a four-velocity field $v$, and also fixes a rotation-rate field $\MatΩ$. It is natural to impose that $u_0=v$. We show that then the spatial triad $(u_p)$ can only be rotating w.r.t. F, and that the title problem is solved if one imposes that the corresponding rotation rate $\MatΞ$ be equal to $\MatΩ$ - or also, if one imposes that $\MatΞ=\Mat{0}$. We also analyze other proposals which aimed at solving the title problem.

32 pages (standard 12pt), including appendices. v2: a minor new remark on pp. 29-30

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Cited by in corpus (10)

• A simpler solution of the non-uniqueness problem of the covariant Dirac theory
• A Modified Method for Deriving Self-Conjugate Dirac Hamiltonians in Arbitrary Gravitational Fields and Its Application to Centrally and Axially Symmetric Gravitational Fields
• Some remarks on quantum mechanics in a curved spacetime, especially for a Dirac particle
• On the non-uniqueness problem of the covariant Dirac theory and the spin-rotation coupling
• Should there be a spin-rotation coupling for a Dirac particle?
• On the Hamiltonian and energy operators in a curved spacetime, especially for a Dirac particle
• Defining the space in a general spacetime
• Pauli equation and charged spin-1/2 particle in a weak gravitational field
• On reference frames and the definition of space in a general spacetime
• Comment on "Spin in an arbitrary gravitational field" arXiv:1308.4552