On the Non-uniqueness Problem of the Covariant Dirac Theory and the Spin-Rotation Coupling
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Gorbatenko and Neznamov [arXiv:1301.7599, 2013] recently claimed the absence of the title problem. In this paper, the reason for that problem is reexplained by using the notions of a unitary transformation and of the mean value of an operator, invoked by them. Their arguments actually aim at proving the uniqueness of a particular prescription for solving this problem. But that prescription is again shown non-unique. Two Hamiltonians in the same reference frame in a Minkowski spacetime, only one of them including the spin-rotation coupling term, are proved to be physically non-equivalent. This confirms that the reality of that coupling should be checked experimentally.
KeywordsDirac Hamiltonian Curved spacetime Unitary transformation Rotating frame
It was noted by M. V. Gorbatenko & V. P. Neznamov (private communication) and by a referee that, in the first version of this paper, it was not accounted for the fact that the energy can usually be subjected to a constant shift. The referee suggested a definition of physically equivalent energy operators which is equivalent to the one given below.
- 1.Gorbatenko, M.V., Neznamov, V.P.: Absence of the non-uniqueness problem of the Dirac theory in a curved spacetime. Spin-rotation coupling is not physically relevant. arXiv:1301.7599v2 [gr-qc]
- 3.Arminjon, M.: A solution of the non-uniqueness problem of the Dirac Hamiltonian and energy operators. Ann. Phys. (Berlin) 523, 1008–1028 (2011). Pre-peer-review version: arXiv:1107.4556v2 [gr-qc]. The equation numbers in the present paper refer to that arXiv version MathSciNetADSCrossRefGoogle Scholar
- 4.Arminjon, M.: Should there be a spin-rotation coupling for a Dirac particle? arXiv:1211.1855v1 [gr-qc]
- 12.Gorbatenko, M.V., Neznamov, V.P.: A modified method for deriving self-conjugate Dirac Hamiltonians in arbitrary gravitational fields and its application to centrally and axially symmetric gravitational fields. arXiv:1107.0844v6 [gr-qc]
- 17.Schulten, K.: Relativistic quantum mechanics. Online course of the University of Illinois at Urbana-Champaign (1999) Google Scholar