Remarks on the Aharonov-Bohm Green function

The deconfinement phase transition as an Aharonov-Bohm effect

A subjective and incomplete list of interesting and unique features of the deconfinement phase transition is presented. Furthermore a formal similarity of the density matrix of the Aharonov-Bohm system and QCD is mentioned, as well.

Propagator for spinless and spin-1/2 Aharonov-Bohm-Coulomb systems

The propagator of the spinless Aharonov-Bohm-Coulomb system is derived by following the Duru-Kleinert method. We use this propagator to explore the spin-1/2 Aharonov-Bohm-Coulomb system which contains a point interaction as a Zeeman term. Incorporation of the self-adjoint extension method into the Green's function formalism properly allows us to derive the finite propagator of the spin-1/2 Aharonov-Bohm-Coulomb system. As a by-product, the relation between the self-adjoint extension parameter and the bare coupling constant is obtained. Bound-state energy spectra of both spinless and spin-1/2 A…

Exact solutions of scalar bosons in the presence of the Aharonov-Bohm and Coulomb potentials in the gravitational field of topological defects

In this paper, we analyzed the relativistic quantum motion of a charged scalar particles in the presence of a Aharonov Bohm and Coulomb potentials in the spacetimes produced by an idealized cosmic strings and global monopoles.

Aharonov-Bohm effect in a Class of Noncommutative Theories

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 $θ$.

The Aharonov-Bohm Effect in Noncommutative Quantum Mechanics

The Aharonov-Bohm (AB) effect in non-commutative quantum mechanics (NCQM) is studied. First, by introducing a shift for the magnetic vector potential we give the Schr$\ddot{o}$dinger equations in the presence of a magnetic field on NC space and NC phase space, respectively. Then by solving the Schr$\ddot{o}$dinger equations, we obtain the Aharonov-Bohm (AB) phase on NC space and NC phase space, respectively.

Bound States of the Hydrogen Atom in the Presence of a Magnetic Monopole Field and an Aharonov-Bohm Potential

In the present article we analyze the bound states of an electron in a Coulomb field when an Aharonov-Bohm field as well as a magnetic Dirac monopole are present. We solve, via separation of variables, the Schrödinger equation in spherical coordinates and we show how the Hydrogen energy spectrum depends on the Aharonov-Bohm and the magnetic monopole strengths. In passing, the Klein-Gordon equation is solved.

Unitarity of the Aharonov-Bohm Scattering Amplitudes

We discuss the unitarity relation of the Aharonov-Bohm scattering amplitude with the hope that it distinguishes between the differing treatments which employ different incident waves. We find that the original Aharonov-Bohm scattering amplitude satisfies the unitarity relation under the regularization prescription whose theoretical foundation does not appear to be understood. On the other hand, the amplitude obtained by Ruijsenaars who uses plane wave as incident wave also satisfies the unitarity relation but in an unusual way.

Aharonov-Bohm Scattering, Contact Interactions and Scale Invariance

We perform a perturbative analysis of the Aharonov-Bohm problem to one loop in a field-theoretic formulation, and show that contact interactions are necessary for renormalizability. In general, the classical scale invariance of this problem is broken quantum mechanically. There exists however a critical point for which this anomaly disappears.

Lorentz violation correction to the Aharonov-Bohm scattering

In this paper, using a (2+1)-dimensional field theory approach, we study the Aharonov-Bohm (AB) scattering with Lorentz symmetry breaking. We obtain the modified scattering amplitude to the AB effect due to the small Lorentz violation correction in the breaking parameter and prove that up to one loop the model is free from ultraviolet divergences.

Relativistic Corrections to the Aharonov-Bohm Scattering

We determine the |p|/m expansion of the two body scattering amplitude of the quantum theory of a Chern-Simons field minimally coupled to a scalar field with quartic self-interaction. It is shown that the existence of a critical value of the self-interaction parameter for which the 2-particle amplitude reduces to the Aharonov-Bohm one is restricted to the leading, nonrelativistic, order. The subdominant terms correspond to relativistic corrections to the Aharonov-Bohm scattering.

The Aharonov-Bohm effect for a knotted magnetic solenoid

We show that the linking of a semiclassical path of a charged particle with a knotted magnetic solenoid results in the Aharonov-Bohm effect. The phase shift in the wave function is proportional to the flux intersecting a certain connected and orientable surface bounded by the knot (a Seifert surface of the knot).

Solutions of relativistic wave equations in superpositions of Aharonov-Bohm, magnetic, and electric fields

We present new exact solutions (in 3+1 and 2+1 dimensions) of relativistic wave equations (Klein-Gordon and Dirac) in external electromagnetic fields of special form. These fields are combinations of Aharonov-Bohm solenoid field and some additional electric and magnetic fields. In particular, as such additional fields, we consider longitudinal electric and magnetic fields, some crossed fields, and some special non-uniform fields. The solutions obtained can be useful to study Aharonov-Bohm effect in the corresponding electromagnetic fields.

On the scattering amplitude in the Aharonov-Bohm gauge field

A general expression for the scattering amplitude of nonrelativistic spinless particles in the Aharonov-Bohm gauge potential is obtained within the time independent formalism. The result is valid also in the backward and forward directions as well as for any choice of the boundary conditions on the wave function at the flux tube position.

Internal Frame Dragging and a Global Analog of the Aharonov-Bohm Effect

It is shown that the breakdown of a {\it global} symmetry group to a discrete subgroup can lead to analogues of the Aharonov-Bohm effect. At sufficiently low momentum, the cross-section for scattering of a particle with nontrivial $\Z_2$ charge off a global vortex is almost equal to (but definitely different from) maximal Aharonov-Bohm scattering; the effect goes away at large momentum. The scattering of a spin-1/2 particle off a magnetic vortex provides an amusing experimentally realizable example.

Comment on Internal Frame Dragging and a Global Analog of the Aharonov-Bohm Effect

It is shown that AB-like cross sections can be obtained from symmetry breaking which does not require infinite energy, angular dependence in the symmetry breaking term, or a nontrivial $Z_2$ charge.

Perturbative Analysis of Nonabelian Aharonov-Bohm Scattering

We perform a perturbative analysis of the nonabelian Aharonov-Bohm problem to one loop in a field theoretic framework, and show the necessity of contact interactions for renormalizability of perturbation theory. Moreover at critical values of the contact interaction strength the theory is finite and preserves classical conformal invariance.

Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential

In this work we study modifications in the Aharonov-Bohm effect for relativistic spin 1/2 particles due to the noncommutativity of spacetime in $2 + 1$ dimensions. The noncommutativity gives rise to a correction to the Aharonov-Bohm potential which is highly singular at the origin, producing divergences in a perturbative expansion around the usual solution of the free Dirac equation. This problem is surmounted by using a perturbative expansion around the exact solution of the \textit{commutative} Aharonov-Bohm problem. We calculate, in this setting, the scattering amplitude and the corrections…

A Global Analogue of the Aharonov-Bohm Effect

This paper has been heavily revised, the final results now being contained in hep-ph/9311202 and hep-ph/9311203.

Aharonov-Bohm Effect on Noncommutative Plane: A Coherent State Approach

We apply the coherent state approach to study Aharonov-Bohm effect in the field theory context. We verify that, contrarily to the commutative result, the scattering amplitude is ultraviolet finite. However, we have logarithmic singularities as the noncommutative parameter tends to zero. Thus, the inclusion of a quartic self-interaction for the scalar field is necessary to obtain a smooth commutative limit.

The Hamiltonian in an Aharonov-Bohm gauge field and its self-adjoint extensions

By using the spherical coordinates in 3+1 dimensions we study the self-adjointness of the Dirac Hamiltonian in an Aharonov-Bohm gauge field of an infinitely thin magnetic flux tube. It is shown that the angular part of the Dirac Hamiltonian requires self-adjoint extensions as well as its radial one. The self-adjoint extensions of the angular part are parametrized by 2x2 unitary matrix.

Discrete Gauge Symmetry and Aharonov-Bohm Radiation in String Theory

We investigate cosmological constraints on phenomenological models with discrete gauge symmetries by discussing the radiation of standard model particles from Aharonov-Bohm strings. Using intersecting D-brane models in Type IIA string theory, we demonstrate that Aharonov-Bohm radiation, when combined with cosmological observations, imposes constraints on the compactification scales.

Radiation of Supersymmetric Particles from Aharonov-Bohm R-string

We study radiation of supersymmetric particles from an Aharonov-Bohm string associated with a discrete R-symmetry. Radiation of the lightest supersymmetric particle, when combined with the observed dark matter density, imposes constraints on the string tension or the freeze-out temperature of the particle. We also calculate the amplitude for Aharonov-Bohm radiation of massive spin $3/2$ particles.

Aharonov--Bohm Effect in 3D Abelian Higgs Theory

We study a field--theoretical analogue of the Aharonov--Bohm effect in the 3D Abelian Higgs Model: the corresponding topological interaction is proportional to the linking number of the vortex and the particle world trajectories. We show that the Aharonov--Bohm effect gives rise to a nontrivial interaction of tested charged particles.

Aharonov-Bohm Effect and Disclinations in an Elastic Medium

In this work we investigate quasiparticles in the background of defects in solids using the geometric theory of defects. We use the parallel transport matrix to study the Aharonov-Bohm effect in this background. For quasiparticles moving in this effective medium we demonstrate an effect similar to the gravitational Aharonov- Bohm effect. We analyze this effect in an elastic medium with one and $N$ defects.

The K-Theoretic Formulation of D-Brane Aharonov-Bohm Phases

The topological calculation of Aharonov-Bohm phases associated with D-branes in the absence of a Neveu-Schwarz B-field is explored. The K-theoretic classification of Ramond-Ramond fields in Type II and Type I theories is used to produce formulae for the Aharonov-Bohm phase associated with a torsion flux. A topological construction shows that K-theoretic pairings to calculate such phases exist and are well-defined. An analytic perspective is then taken, obtaining a means for determining Aharonov-Bohm phases by way of the reduced eta-invariant. This perspective is used to calculate the phase for…

Electron-positron pair production in the Aharonov-Bohm potential

In the framework of QED we evaluate the cross section for electron-positron pair production by a single photon in the presence of the external Aharonov-Bohm potential in first order of perturbation theory. We analyse energy, angular and polarization distributions at different energy regimes: near the threshold and at high photon energies.

深化引力阿哈罗诺夫-玻姆效应研究

Sharpening the Gravitational Aharonov-Bohm effect

本研究以复标量场这一经典系统的引力Aharonov-Bohm效应类比为对象，证明该效应原则上与量子力学无关，并探讨了经典场描述与标准单粒子量子描述的关联。

The Aharonov-Casher Theorem and the Axial Anomaly in the Aharonov-Bohm Potential

The spectral properties of the Dirac Hamiltonian in the the Aharonov-Bohm potential are discussed. By using the Krein-Friedel formula, the density of states (DOS) for different self-adjoint extensions is calculated. As in the nonrelativistic case, whenever a bound state is present in the spectrum it is always accompanied by a (anti)resonance at the energy. The Aharonov-Casher theorem must be corrected for singular field configurations. There are no zero (threshold) modes in the Aharonov-Bohm potential. For our choice of the 2d Dirac Hamiltonian, the phase-shift flip is shown to occur at only p…

Aharonov-Bohm Scattering of a Localized Wave Packet: Analysis of the Forward Direction

The Aharonov-Bohm scattering of a localized wave packet is considered. A careful analysis of the forward direction points out new results: according to the time-dependent solution obtained by means of the asymptotic representation for the propagator (kernel), a phenomenon of auto-interference occurs along the forward direction, where, also, the probability density current is evaluated and found finite.

Aharonov-Bohm Effect and Hidden Photons

Signs of hypothetical light gauge bosons from a hidden sector may appear in Aharonov-Bohm-like experiments. The absence of signal in carried on experiments allow us to set a modest constraint to the mass and coupling constant of these particles. Our findings open the possibility to exploit the leaking of hidden magnetic field in a different setup of experiments.

Gravitational Aharonov-Bohm effect due to noncommutative BTZ black hole

In this paper we consider the scattering of massless planar scalar waves by a noncommutative BTZ black hole. We compute the differential cross section via the partial wave approach, and we mainly show that the scattering of planar waves leads to a modified Aharonov-Bohm effect due to spacetime noncommutativity

柴郡猫 θ 项、Aharonov-Bohm 效应与轴子

Cheshire $θ$ terms, Aharonov-Bohm effects, and axions

本文提出场论中与全局涡旋相关的“柴郡猫 θ 项”，说明其可使绕涡旋粒子产生 Aharonov-Bohm 效应，并以轴子耦合 QCD 中绕轴子弦的重子、轻子为例。

Nucleon Statistics in Holographic QCD : Aharonov-Bohm Effect in a Matrix Model

We show that the Aharonov-Bohm effect in the nuclear matrix model derives the statistical nature of nucleons in holographic QCD. For N_c= odd (even), the nucleon is shown to be a fermion (boson).

Bound states of massive fermions in the Aharonov--Bohm-like fields

Bound states of massive fermions in the Aharonov-Bohm like fields have analytically been studied. The Hamiltonians with the Aharonov--Bohm like potentials are essentially singular and therefore require specification of a one-parameter self-adjoint extension. We construct self-adjoint Dirac Hamiltonians with the Aharonov-Bohm (AB) potential in 2+1 dimensions that are specified by boundary conditions at the origin. It is of interest that for some range of extension parameter the AB potential can bind relativistic charged massive fermions. The bound-state energy is determined by the AB magnetic f…

Hidden superconformal symmetry of spinless Aharonov-Bohm system

A hidden supersymmetry is revealed in the spinless Aharonov-Bohm problem. The intrinsic supersymmetric structure is shown to be intimately related with the scale symmetry. As a result, a bosonized superconformal symmetry is identified in the system. Different self-adjoint extensions of the Aharonov-Bohm problem are studied in the light of this superconformal structure and interacting anyons. Scattering problem of the original Aharonov-Bohm model is discussed in the context of the revealed supersymmetry.

Effect of Aharonov-Bohm Phase on Spin Tunneling

The role of Aharonov-Bohm effect in quantum tunneling is examined when a potential is defined on the $S^1$ and has $N$-fold symmetry. We show that the low-lying energy levels split from the $N$-fold degenerate ground state oscillate as a function of the Aharonov-Bohm phase, from which general degeneracy conditions depending on the magnetic flux is obtained. We apply these results to the spin tunneling in a spin system with $N$-fold rotational symmetry around a hard axis.

Aharonov-Bohm effect on the Poincaré disk

We consider formal quantum hamiltonian of a charged particle on the Poincaré disk in the presence of an Aharonov-Bohm magnetic vortex and a uniform magnetic field. It is shown that this hamiltonian admits a four-parameter family of self-adjoint extensions. Its resolvent and the density of states are calculated for natural values of the extension parameters.

Aharonov-Bohm interactions of a vector unparticle

Recently Georgi argued that hypothetical conformally invariant hidden sector weakly interacting with ordinary particles will have unusual manifestations at low energies in terms of effective degrees of freedom called unparticles. In this note we consider Aharonov-Bohm type of interactions due to the vector unparticle coupled to elementary fermions. We have found that quantum mechanical phase shift is path-dependent.

Magnetic Catalysis of Dynamical Symmetry Breaking and Aharonov-Bohm Effect

The phenomenon of the magnetic catalysis of dynamical symmetry breaking is based on the dimensional reduction $D\to D-2$ in the dynamics of fermion pairing in a magnetic field. We discuss similarities between this phenomenon and the Aharonov-Bohm effect. This leads to the interpretation of the dynamics of the (1+1)-dimensional Gross-Neveu model with a non-integer number of fermion colors as a quantum field theoretical analogue of the Aharonov-Bohm dynamics.

Aharonov-Bohm phase for an electromagnetic wave background

The canonical Aharonov-Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov-Bohm phase acquired by a charged particle moving in {\it time-dependent} potentials . In particular, we focus on the case of a charged particle moving in the time varying field of a plane electromagnetic wave. We work out the Aharonov-Bohm phase using both the potential ({\it i.e.} $\oint A_μdx ^μ$) and field ({\it i.e.} $\frac{1}{2}\int F_{μν} d σ^{μν}$) forms of the Aharanov-Bohm phase. We give conditions in terms of the parameters of the system (frequency of the …

Nonassociativity, Dirac monopoles and Aharonov-Bohm effect

The Aharonov-Bohm (AB) effect for the singular string associated with the Dirac monopole carrying an arbitrary magnetic charge is studied. It is shown that the emerging difficulties in explanation of the AB effect may be removed by introducing nonassociative path-dependent wave functions. This provides the absence of the AB effect for the Dirac string of magnetic monopole with an arbitrary magnetic charge.

The Aharonov-Bohm Effect on Entanglement Entropy in Conformal Field Theory

We consider the Aharonov-Bohm effect on entanglement entropy for one interval in (1+1) dimensional conformal field theory on a one dimensional ring. The magnetic field is confined inside the ring, i.e. there is a Wilson loop on the ring. The Aharonov-Bohm phase factor which is proportional to the Wilson loop is represented as insertion of twist operators. We compute exactly the Renyi entropy from a four point function of twist operators in a free charged scalar field.

Vortex vs spinning string: Iordanskii force and gravitational Aharonov-Bohm effect

We discuss the transverse force acting on the spinning cosmic string, moving in the background matter. It comes from the gravitational Aharonov-Bohm effect and corresponds to the Iordanskii force acting on the vortex in superfluids, when the vortex moves with respect to the normal component of the liquid.

Aharonov-Bohm Effect in Lattice Abelian Higgs Theory

We study a field-theoretical analogue of the Aharonov-Bohm effect in two-, three- and four-dimensional Abelian Higgs models; the corresponding topological interaction is proportional to the linking number of the Abrikosov vortex and the particle world trajectories. We show that the Aharonov-Bohm effect gives rise to a nontrivial interaction of charged test particles. The numerical calculations in the three-dimensional model confirm this fact.

Hydrino like states in graphene and Aharonov-Bohm field

We study the dynamics of fermions on graphene in presence of Coulomb impurities and Aharonov-Bohm field. Special emphasis is given to the formation of hydrino like states and its lifting of degeneracy due to the presence of AB field. The flux of the AB field can be tuned to make the low angular momentum hydrino states stable against decay. The zero limit physics of the two coupling constants α_G and Φinvolved in the system is discussed.