QUANTIZATION AND SUPERSELECTION SECTORS II: DIRAC MONOPOLE AND AHARONOV-BOHM EFFECT

1990 ◽  
Vol 02 (01) ◽  
pp. 73-104 ◽  
Author(s):  
N.P. LANDSMAN
Keyword(s):  
General Procedure ◽  
Preceding Paper ◽  
Quantum Effects ◽  
Magnetic Monopoles ◽  
Unitary Representations ◽  
Dirac Monopole ◽  
Topological Quantum ◽  
Bohm Effect ◽  
The Given ◽  
Aharonov Bohm

The quantization procedure of the preceding paper is applied to study two generic topological quantum effects, viz. the charge quantization induced by (abelian) magnetic monopoles, and the Aharonov-Bohm effect. Prior to these applications, a general procedure is given for reducing unitary representations of a locally compact G which are induced by nontrivial unitary representations of H⊂G. This involves the use of spherical trace functions, and is useful in the determination of the eigenfunctions of the Hamiltonian of the particle in a given superselection sector. Such Hamiltonians, implementing the time-evolution on the given abstract C*-algebra, are explicitly constructed and analyzed. The relevant quantum effects are found to be a consequence of the representation theory of the appropriate algebras of observables. In this way a group- and operator-theoretic elucidation of the mathematical structure of the given systems is attempted. This paper may be read independently of its predecessor.

Monopole charge quantization and the Aharonov–Bohm effect

1984 ◽  
Vol 62 (8) ◽  
pp. 737-740 ◽  
Author(s):  
G. Kunstatter
Keyword(s):  
Long Range ◽  
Quantization Condition ◽  
Simple Derivation ◽  
Asymptotic Field ◽  
Dirac Monopole ◽  
Charge Quantization ◽  
Bohm Effect ◽  
Field Lines ◽  
Aharonov Bohm ◽  
Electrically Charged

We present a simple derivation of the Dirac monopole charge quantization condition, making explicit use of the Aharonov–Bohm effect. Since only the asymptotic field lines of the monopole play a crucial role, this derivation clearly shows that the quantization condition must hold unless the electrically charged particle and the monopole exchange new long-range forces. In particular, this implies that Cabrera's monopole event would be consistent with Fairbank's observations of free quarks only if the monopole carried long-range (unconfined) colour-magnetic fields.

Topological quantum scattering under the influence of a nontrivial boundary condition

2016 ◽  
Vol 31 (11) ◽  
pp. 1650074 ◽  
Author(s):  
Herondy Mota
Keyword(s):  
Boundary Condition ◽  
Phase Shift ◽  
Gordon Equation ◽  
Scattering Problem ◽  
Quantum Scattering ◽  
Topological Quantum ◽  
Klein Gordon ◽  
Bohm Effect ◽  
Aharonov Bohm

We consider the quantum scattering problem of a relativistic particle in (2 + 1)-dimensional cosmic string spacetime under the influence of a nontrivial boundary condition imposed on the solution of the Klein–Gordon equation. The solution is then shifted as consequence of the nontrivial boundary condition and the role of the phase shift is to produce an Aharonov–Bohm-like effect. We examine the connection between this phase shift and the electromagnetic and gravitational analogous of the Aharonov–Bohm effect and compare the present results with previous ones obtained in the literature, also considering non-relativistic cases.

scholarly journals Aharonov-Bohm Effect vs. Dirac Monopole: A-B ⇔ D

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Miguel Socolovsky ◽  
Keyword(s):  
Dirac Monopole ◽  
Bohm Effect ◽  
Aharonov Bohm

scholarly journals Aharonov–Bohm superselection sectors

2020 ◽  
Vol 110 (12) ◽  
pp. 3243-3278
Author(s):  
Claudio Dappiaggi ◽  
Giuseppe Ruzzi ◽  
Ezio Vasselli
Keyword(s):  
Fundamental Group ◽  
Quantum Number ◽  
Minkowski Spacetime ◽  
Dirac Field ◽  
Topological Quantum ◽  
Hyperbolic Spacetime ◽  
Bohm Effect ◽  
Local Observables ◽  
Aharonov Bohm ◽  
Natural Description

AbstractWe show that the Aharonov–Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labelling charged superselection sectors. In the present paper, we show that this “topological” quantum number amounts to the presence of a background flat potential which rules the behaviour of charges when transported along paths as in the Aharonov–Bohm effect. To confirm these abstract results, we quantize the Dirac field in the presence of a background flat potential and show that the Aharonov–Bohm phase gives an irreducible representation of the fundamental group of the spacetime labelling the charged sectors of the Dirac field. We also show that non-Abelian generalizations of this effect are possible only on spacetimes with a non-Abelian fundamental group.

scholarly journals NONASSOCIATIVITY, DIRAC MONOPOLE AND AHARONOV–BOHM EFFECT

2007 ◽  
Vol 04 (05) ◽  
pp. 717-726 ◽  
Author(s):  
ALEXANDER I. NESTEROV
Keyword(s):  
Magnetic Monopole ◽  
Magnetic Charge ◽  
Dirac Monopole ◽  
Bohm Effect ◽  
Path Dependent ◽  
Aharonov Bohm

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 wavefunctions. Our results imply that the Dirac singular string escapes detection in the AB experiment even for an arbitrary charged magnetic monopole.

Phenomena and devices at the quantum scale and the mesoscale

2017 ◽  
Author(s):  
Sandip Tiwari
Keyword(s):  
Coulomb Blockade ◽  
Secure Communication ◽  
Quantum Hall ◽  
Nanoscale Device ◽  
Self Energy ◽  
Stability Diagrams ◽  
Charge Stability ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Non Locality

Unique nanoscale phenomena arise in quantum and mesoscale properties and there are additional intriguing twists from effects that are classical in origin. In this chapter, these are brought forth through an exploration of quantum computation with the important notions of superposition, entanglement, non-locality, cryptography and secure communication. The quantum mesoscale and implications of nonlocality of potential are discussed through Aharonov-Bohm effect, the quantum Hall effect in its various forms including spin, and these are unified through a topological discussion. Single electron effect as a classical phenomenon with Coulomb blockade including in multiple dot systems where charge stability diagrams may be drawn as phase diagram is discussed, and is also extended to explore the even-odd and Kondo consequences for quantum-dot transport. This brings up the self-energy discussion important to nanoscale device understanding.

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