On the generally covariant Dirac equation

Chapman, Tim C.; Leiter, D.

doi:10.1119/1.10256

Cited by 46 publications

(72 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…However, usually the (γ µ ) field is deduced from a tetrad field and from a constant set of "flat" Dirac matrices (γ ♯α ) as in Eq. (10). Then any hermitizing matrix for the set (γ ♯α ) is also a (constant) hermitizing matrix A for the (γ µ ) field [25].…”

Section: Dirac Hamiltonian Operator In a General Spacetimementioning

confidence: 99%

“…Until recently, the choice of the tetrad field has been assumed to be entirely neutral, because the Lagrangian of the standard covariant Dirac equation is invariant under a change of the tetrad field, hence the DFW equations obtained with any two different tetrad fields are equivalent [9,10]. (This is true in a topologically-simple spacetime [11].)…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Should There Be a Spin-Rotation Coupling for a Dirac Particle?

Arminjon

2014

Int J Theor Phys

View full text Add to dashboard Cite

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.

show abstract

Section: Dirac Hamiltonian Operator In a General Spacetimementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Should There Be a Spin-Rotation Coupling for a Dirac Particle?

Arminjon

2014

Int J Theor Phys

View full text Add to dashboard Cite

show abstract

“…(6) leads to different mean values for H and H in the time-dependent case. However, it was not obvious that the condition(8)is indeed necessary to the equality of all mean values, i.e., to the validity of Eq (7)…”

mentioning

confidence: 99%

On the Hamiltonian and energy operators in a curved spacetime, especially for a Dirac particle

Arminjon

2015

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

On the Hamiltonian and energy operators in a curved spacetime, especially for a Dirac particle Abstract. The definition of the Hamiltonian operator H for a general wave equation in a general spacetime is discussed. We recall that H depends on the coordinate system merely through the corresponding reference frame. When the wave equation involves a gauge choice and the gauge change is time-dependent, H as an operator depends on the gauge choice. This dependence extends to the energy operator E, which is the Hermitian part of H. We distinguish between this ambiguity issue of E and the one that occurs due to a mere change of the "representation" (e.g. transforming the Dirac wave function from the "Dirac representation" to a "Foldy-Wouthuysen representation"). We also assert that the energy operator ought to be well defined in a given reference frame at a given time, e.g. by comparing the situation for this operator with the main features of the energy for a classical Hamiltonian particle. IntroductionThe quantum effects in the classical gravitational field which have been observed on Earth for neutrons and for atoms (e.g. [1,2,3,4,5]) are quantum-mechanical effects. That is, they were predicted (before their observation) by using "first-quantized" theory. They are, to this author's knowledge, the only observed effects of the gravity-quantum coupling. Thus, QM in a curved spacetime covers all currently available experiments about the interaction between gravity and the quantum. Neutrons are spin half particles, and spin half particles are normally described by the Dirac equation. Moreover, besides observing directly the quantum behaviour of particles in a gravitational field, one also would like to account for the influence of the gravitational field on, for example, the quantum behaviour of particles in an electromagnetic field, e.g. the behaviour of electrons in an atom. (This influence is very small in the very weak gravitational field that we have in the solar system, of course. Yet it is expected to be important in strong gravitational fields.) Therefore, QM of the (generally-)covariant Dirac equation is quite an important chapter of curved-spacetime QM. The covariant Dirac equation involves the choice, at any point X in spacetime (and depending smoothly on X), of an orthonormal basis of the tangent space at that point X. I.e., it involves the choice of a tetrad field [6,7]. This plays the role of a gauge field. Indeed, the two realizations of the covariant Dirac equation that are got with two different tetrad fields are equivalent, at least locally [8]. However, it has been proved in recent years that the Hamiltonian operator associated, in a given coordinate system, with the covariant Dirac equation, does depend on the choice of the tetrad field. In particular, the energy spectrum and the energy mean values depend on that choice [9,10], and so does the presence or absence of Mashhoon's spin-rotation coupling term [11,12].

show abstract

“…In the rotational coordinate system (t,x,y,z), the tetrad components can be obtained from the following line element (c.f. [2,3])…”

Section: The Rotation-spin Effect In the Parallelism Descriptionmentioning

confidence: 99%

“…Recently the spin-rotation-gravity coupling has been paid much attention and appeared in the work of many authors who have been mainly interested in the study of wave equations in accelerated systems and gravitational fields [1][2][3][4][5][6][7][8]. Indeed, the coupling under consideration here directly involves wave effects that pertain to the physical foundations of general relativity.…”

Section: Introductionmentioning

confidence: 99%

Rotation Intrinsic Spin Coupling: The Parallelism Description

Zhang

Беешам

2001

Mod. Phys. Lett. A

View full text Add to dashboard Cite

For the Dirac particle in the rotational system, the rotation induced inertia effect is analogously treated as the modification of the "spin connection" on the Dirac equation in the flat spacetime, which is determined by the equivalent tetrad. From the point of view of parallelism description of spacetime, the obtained torsion axial-vector is just the rotational angular velocity, which is included in the "spin connection". Furthermore the axial-vector spin coupling induced spin precession is just the rotation-spin(1/2) interaction predicted by Mashhoon. Our derivation treatment is straightforward and simplified in the geometrical meaning and physical conception, however the obtained conclusions are consistent with that of the other previous work.

show abstract

On the generally covariant Dirac equation

Cited by 46 publications

References 0 publications

Should There Be a Spin-Rotation Coupling for a Dirac Particle?

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

Rotation Intrinsic Spin Coupling: The Parallelism Description

Contact Info

Product

Resources

About