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Title: Global analogue of the Aharonov-Bohm effect

Abstract

This thesis deals with a global analogue of the Aharonov-Bohm effect previously pointed out by other authors. The effect was not well understood because the pure Aharonov-Bohm cross section was thought to be merely an approximate low energy limit. This thesis provides a detailed analysis and reveals that in the particular model considered, there is an exact Aharonov-Bohm cross section over the energy range that a mass splitting occurs. At energies slightly above the mass splitting, the effect has completely disappeared and there is effectively no scattering at large distances. This is a curious observation as it was previously thought that a global theory would not act exactly like a local one over an extended range of energies. It begs the heretical speculation that experimentally observed forces modelled with Lagrangians possessing local symmetries may have an underlying global theory.

Authors:
Publication Date:
Research Org.:
California Inst. of Tech., Pasadena, CA (United States)
OSTI Identifier:
39349
Resource Type:
Miscellaneous
Resource Relation:
Other Information: TH: Thesis (Ph.D.); PBD: 1993
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; AHARONOV-BOHM EFFECT; GLOBAL ANALYSIS; LAGRANGIAN FIELD THEORY

Citation Formats

Navin, R.L. Global analogue of the Aharonov-Bohm effect. United States: N. p., 1993. Web.
Navin, R.L. Global analogue of the Aharonov-Bohm effect. United States.
Navin, R.L. 1993. "Global analogue of the Aharonov-Bohm effect". United States. doi:.
@article{osti_39349,
title = {Global analogue of the Aharonov-Bohm effect},
author = {Navin, R.L.},
abstractNote = {This thesis deals with a global analogue of the Aharonov-Bohm effect previously pointed out by other authors. The effect was not well understood because the pure Aharonov-Bohm cross section was thought to be merely an approximate low energy limit. This thesis provides a detailed analysis and reveals that in the particular model considered, there is an exact Aharonov-Bohm cross section over the energy range that a mass splitting occurs. At energies slightly above the mass splitting, the effect has completely disappeared and there is effectively no scattering at large distances. This is a curious observation as it was previously thought that a global theory would not act exactly like a local one over an extended range of energies. It begs the heretical speculation that experimentally observed forces modelled with Lagrangians possessing local symmetries may have an underlying global theory.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 1993,
month =
}

Miscellaneous:
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  • The Aharonov-Bohm effect is a celebrated quantum mechanical effect which some have claimed is an example of non-locality, i.e., of action at a distance. This thesis examines the theory and experimental tests of the effect, and compares it to another supposed example of non-locality, the EPR correlations. The role of the electromagnetic potentials in the quantum formalism, and especially gauge invariance and the physical significance of the vector potential, is detailed. The author argues that K.H. Yang's proofs of the gauge arbitrariness of the conventional formalism are mistaken. Four central and conflicting theories of the AB effect are reviewed andmore » critiqued: (i) physically significant potentials, (ii) local effects of electromagnetic fluxes, (iii) multi-valued wave functions, and (iv) non-locality. An entire chapter is devoted to the topological interpretations of the effect which model the potentials as connections in higher-dimensional fiber bundle geometries. The relation between the AB effect and geometric phase phenomena, like Berry's phase, is studied. The new geometric models inherit the merits and demerits of the potentials interpretation. The quantum no-signalling proofs for the case of the EPR-Bohm-Bell experiments are analyzed and unified in a single theorem: they are simple consequences of the tensor product representation of combined quantum systems. All proposed local theories of the AB effect are finally unsatisfactory-for a variety of reasons. However, given the lack of of a clear criterion for non-locality, there are no decisive grounds for the claim that the AB effect is non-local.« less
  • Using the path-ordered products of the relevant affine connection we examine the effect of the parallel transport of vectors and spinors (three-dimensional case only) around closed paths (circles) in the field corresponding to the cylindrically symmetric cosmic string. We compute the solution for three-dimensional gravity also.
  • It is shown that the breakdown of a {ital global} symmetry group to a discrete subgroup can lead to analogs of the Aharonov-Bohm effect. At sufficiently low momentum transfer, the cross section for scattering of a particle with nontrivial Z{sub 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 transfer. The scattering of a spin-1/2 particle off a magnetic vortex provides an amusing experimentally realizable example.
  • We discuss the Aharonov-Bohm effect of a magnetic flux for its influence on a two-dimensional quantum cloak. It is shown that the matter wave of a charged particle under the global influence of the Aharonov-Bohm effect can still be perfectly cloaked and guided by the quantum cloak. Since the presence of the global influence of a magnetic flux on charged particles is universal, the perfect cloaking and guiding nature not only provides an ideal setup to cloak an object from matter waves but also provides an ideal setup to test the global physics of charged matter waves in the presencemore » of a bare magnetic flux.« less
  • The scattering of relativistic spin-1/2 neutral particles with a magnetic dipole moment by a long straight charged line and a magnetic flux line at the same position is studied. The scattering cross sections for unpolarized and polarized particles are obtained by solving the Dirac-Pauli equation. The results are in general the same as those for pure Aharonov-Casher scattering (by the charged line alone) as expected. However, in special cases when the incident energy, the line charge density, and the magnetic flux satisfy some relations, the cross section for polarized particles is dramatically changed. Relations between the polarization of incident particlesmore » and that of scattered ones are presented, both in the full relativistic case and the nonrelativistic limit. The characteristic difference between the general and special cases lies in the backward direction: in the general cases the incident particles are simply bounced while in the special cases their polarization is turned over simultaneously. For pure Aharonov-Casher scattering there exist cases where the helicities of all scattered particles are reversed. This seems to be remarkable but appears unnoticed previously. Two mathematical approaches are employed to deal with the singularity of the electric and magnetic field and it turns out that the physical results are essentially the same.« less