Helicity and the Aharonov-Bohm effect

Vera, Francisco; Schmidt, Iván

doi:10.1103/physrevd.42.3591

Cited by 26 publications

(21 citation statements)

References 15 publications

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“…Subsequently this interaction was attributed to a spin-magnetic moment interaction [6]. The first order Born amplitude for a Dirac particle was calculated in [7] and the second order in [8] where full agreement with the expansions of the exact amplitude [9] to the corresponding order was found. Non-relativistic perturbative calculations within the framework of the field theory models of the AB with spin-1/2 particles suffered no problems [10,11].…”

Section: Introductionmentioning

confidence: 84%

Partial wave analysis of the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential

Shikakhwa

Pak

2003

Phys. Rev. D

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A partial wave analysis using the basis of the total angular momentum operator J3 is carried out for the first order Born amplitude of a Dirac particle in an Aharonov-Bohm (AB) potential. It is demonstrated that the s-partial wave contributes to the scattering amplitude in contrast to the case with scalar non-relativistic particles. We suggest that this explains the fact that the first order Born amplitude of a Dirac particle coincides with the exact amplitude expanded to the same order, where it does not for a scalar particle. An interesting algebra involving the Dirac velocity operator and the angular observables is discovered and its consequences are exploited.

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Section: Introductionmentioning

confidence: 84%

Partial wave analysis of the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential

Shikakhwa

Pak

2003

Phys. Rev. D

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“…We see from (18) that the vector potential in the noncommutative plane has a component in the radial direction (u r ) which is not present in the standard case. In fact, in polar coordinates we can write…”

Section: The Aharonov-bohm Potential In the Noncommutative Planementioning

confidence: 99%

Aharonov-Bohm effect in a class of noncommutative theories

et al. 2011

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The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in θ, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schrödinger-Pauli equation is separable through successive unitary transformations and the exact solution is found. The scattering amplitude is calculated and compared with the usual case. In the noncommutative Aharonov-Bohm case the differential cross section is independent of θ.

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“…Many approaches were suggested in the literature to remedy this problem for non-relativistic particles, examples of which are [2,4,6,[9][10][11][12][13][14]. When the spin degree of freedom is taken into account [8], it was shown that perturbation theory works for both non-relativistic [13] and relativistic particles [3,16,17]; thanks to the spin-magnetic moment interaction.…”

Section: Introductionmentioning

confidence: 99%

The Spin Interaction of a Dirac Particle in an Aharonov-Bohm Potential in First Order Scattering

Albeed

Shikakhwa

2008

Int J Theor Phys

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For a Dirac particle in an Aharonov-Bohm (AB) potential, it is shown that the spin interaction (SI) operator which governs the transitions in the spin sector of the first order S-matrix is related to one of the generators of rotation in the spin space of the particle. This operator, which is given by the projection of the spin operator along the direction of the total momentum of the system, and the two operators constructed from the projections of the operator along the momentum transfer and the z-directions close the SU (2) algebra. It is suggested, then, that these two directions of the total momentum and the momentum transfer form some sort of natural intrinsic directions in terms of which the spin dynamics of the scattering process at first order can be formulated conveniently. A formulation and an interpretation of the conservation of helicity at first order using the spin projection operators along these directions is presented.

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Helicity and the Aharonov-Bohm effect

Cited by 26 publications

References 15 publications

Partial wave analysis of the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential

Partial wave analysis of the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential

Aharonov-Bohm effect in a class of noncommutative theories

The Spin Interaction of a Dirac Particle in an Aharonov-Bohm Potential in First Order Scattering

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