Should there be a spin-rotation coupling for a Dirac particle?

Abstract

It was argued by Mashhoon that a spin-rotation coupling term should add to the Hamiltonian operator in a rotating frame, as compared with the one in an inertial frame. For a Dirac particle, the Hamiltonian and energy operators H and E were recently proved to depend on the tetrad field. We argue that this non-uniqueness of H and E really is a physical problem. We compute the energy operator in the inertial and the rotating frame, using three tetrad fields: one for each of two frameworks proposed to select the tetrad field so as to solve this non-uniqueness problem, and one proposed by Ryder. We find that Mashhoon's term is there if the tetrad rotates as does the reference frame --- but then it is also there in the energy operator for the inertial frame. In fact, the Dirac Hamiltonian operators in two reference frames in relative rotation, but corresponding to the same tetrad field, differ only by the angular momentum term. If the Mashhoon effect is to exist for a Dirac particle, the tetrad field must be selected in a specific way for each reference frame.

29 pages in standard 12pt. V2: Introduction reinforced. New Section 3 on the dependences of the Hamiltonian on the reference frame and on the tetrad field. New references

References in corpus (6)

• On reference frames in spacetime and gravitational energy in freely falling frames
• Quantum Interference Effects in Slowly Rotating NUT Space-time
• General reference frames and their associated space manifolds
• Main effects of the Earth's rotation on the stationary states of ultra-cold neutrons
• A simpler solution of the non-uniqueness problem of the covariant Dirac theory
• On the non-uniqueness problem of the covariant Dirac theory and the spin-rotation coupling

Cited by in corpus (4)

• Spin - Rotation Coupling Observed in Neutron Interferometry
• Local Lorentz transformations and Thomas effect in general relativity
• Some remarks on quantum mechanics in a curved spacetime, especially for a Dirac particle
• On the Hamiltonian and energy operators in a curved spacetime, especially for a Dirac particle