Nonassociativity, Dirac Monopole and Aharonov–bohm Effect

Nesterov, Alexander I.

doi:10.1142/s0219887807002259

Cited by 4 publications

(10 citation statements)

References 38 publications

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“…Thus, we see that the AB effect requires more careful analysis, if we assume existence of an arbitrary monopole charge. The emerging difficulties in explanation of the AB effect may be removed by introducing nonassociative path-dependent wave function Ψ(r; γ), that provides the absence of the AB effect for an arbitrary magnetic charge [22,62].…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Infinite-dimensional representations of the rotation group and Dirac monopole problem

Nesterov

Cruz

2008

Journal of Mathematical Physics

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Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details. Irreducible infinite-dimensional representations, being realized in the indefinite metric Hilbert space, are given by linear unbounded operators in infinite-dimensional topological spaces, supplied with a weak topology and associated weak convergence. We argue that an arbitrary magnetic charge is allowed, and the Dirac quantization condition can be replaced by a generalized quantization rule yielding a new quantum number, the so-called topological spin, which is related to the weight of the Dirac string.

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Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Infinite-dimensional representations of the rotation group and Dirac monopole problem

Nesterov

Cruz

2008

Journal of Mathematical Physics

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“…This situation has been studied by Bruno (2004). As mentioned earlier when Dirac monopoles are non-quantized, we will have a contribution of the evolution around the Dirac string, which will now be 'visible' unless we impose certain extra conditions such as the non-associativity of the path-dependent wave function (Nesterov 2004(Nesterov , 2007. Let us consider the magnetic field B associated with a Dirac monopole given by…”

Section: Anisotropic Spin System Non-quantized Dirac Monopole and Thmentioning

confidence: 99%

“…In recent times, several authors (Bruno 2004;Nesterov 2004Nesterov , 2007 have pointed out that the quantization of the monopole charge is not sacrosanct, as the requirement of spacial isotropy may be lifted in some specific phenomena.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic spin system, quantized Dirac monopole and the Berry phase

Bandyopadhyay

2010

Proc. R. Soc. A.

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The Berry phase, acquired by an anisotropic spin system with spin J ≥ 1 when it is adiabatically rotated in a closed circuit, is considered to be associated with a nonquantized Dirac monopole, and has a geometrical as well as a topological component owing to the Dirac string. Here, it is argued that the Berry phase of a spin state with J ≥ 1 can be associated with a quantized Dirac monopole when the corresponding spin is taken to be an entangled state of a composite system of 1/2 spins. Evidently, this avoids the contribution of the Dirac string, and the Berry phase is purely geometrical in nature.

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“…The examples given below play an important role in the description of generalized coherent states, Thomas precession and nonassociative geometry [7,22,23,24,25,26,27].…”

Section: Examplesmentioning

confidence: 99%

“…During the last few decades, nonassociative structures have been employed in various fields of modern physics. Among others, one may mention the rise of nonassociative objects such as 3-cocycles, which are linked with violations of the Jacobi identity in anomalous quantum field theory, and quantum mechanics with the Dirac monopole, the appearance of Lie groupoids and algebroids in the context of Yang-Mills theories, and the application of nonassociative algebras to gauge theories on commutative but nonassociative fuzzy spaces [1,2,3,4,5,6,7,8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%