Aharonov–Bohm effect for a fermion field in a planar black hole “spacetime”

Abstract

In this paper we consider the dynamics of a massive spinor field in the background of the acoustic black hole spacetime. Although this effective metric is acoustic and describes the propagation of sound waves, it can be considered as a toy model for the gravitational black hole. In this manner, we study the properties of the dynamics of the fermion field in this "gravitational" rotating black hole as well as the vortex background. We compute the differential cross section through the use of the partial wave approach and show that an effect similar to the gravitational AharonovBohm effect occurs for the massive fermion field moving in this effective metric. We discuss the limiting cases and compare the results with the massless scalar field case.

Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space

“…Such a model was originally proposed to address the infinity problem in quantum field theory [1,2], and was shown later that similar property can also appear both in string theory embedded in a background magnetic field [3], and quantum gravity [4]. It has been shown that the rotational symmetry can be broken [5,6], and consquentlly the energy levels of hydrogen atom [7] and Rydberg atoms [8], and topological phase effects [9][10][11] as well as the quantum speed of relativistic charged particles [12][13][14][15] and fluid [16] can receive interesting corrections. The algebra (1) can be accomplished by a replacement x µ → x µ + p µ /(2 ).…”

Dirac field in the background of a planar defect

“…To find the phase shift we need only to study the behavior of the solutions for large distances. Therefore, we can expand the functions for large r [29]. At this point we need to know the behavior of the defect solution which is driven by the field φ, so we turn attention to the bosonic sector of the model to proceed.…”

Probing noncommutativities of phase space by using persistent charged current and its asymmetry

“…This Lagrangian is gauge invariant because the noncommutative corrections depend only on the covariant derivative D β NC and the electromagnetic field strength F μν NC . Therefore, the noncommutative corrections on the Aharonov-Bohm phase shift can be defined unambiguously [28][29][30][31][32][33] and can be interpreted consistently on the commutative and noncommutative phase spaces. The equation of motion can be obtained directly from this Lagrangian as…”

“…It has been shown in Refs. [28][29][30][31][32][33][34][35][36][37][38] that magnetic flux due to the permanent dipole moment can modify the Aharonov-Bohm effect [39] as well as the Aharonov-Casher effect [40]. Furthermore, the magnetic flux can also generate a persistent charged current in a metal ring.…”