Magnetic monopoles with generalized quantization condition

Abstract

Theory of pointlike magnetic monopole with an arbitrary magnetic charge is considered. It is shown that a proper description requires making use of nonunitary representations of the rotation group and the nonassociative generalization of the gauge group and fibre bundle theory.Comment: REVTEX4 file, 6 pages. To appear in Physics Letters

On Observability of Dirac's String

“…29 −µ form the basis of the representation bounded below D + ( , −µ). 32 In general, the obtained solutions are being given by non-square integrable functions on the sphere belong to the extended Hilbert space H η , where the inner product is defined by the bilinear form of the type (ψ, ψ ) η = (ψ, ηψ ) = ψ ηψ dµ(x) (15) such that the norm is positive, (ψ, ψ) η > 0.…”

“…Nevertheless, the self-consistent theory of Dirac's monopole with an arbitrary magnetic charge can be constructed by considering the nonassociative fiber bundle theory and nonassociative generalization of the Hopf bundle. [27][28][29][30] In the context of the group theory one has to involve infinite-dimensional representations of the rotation group to provide a consistent description of non-quantized Dirac monopole. 29,31,32 Recently, the non-quantized "magnetic" monopoles arising in trapped Λ-type atoms and anisotropic spin systems has been reported in Refs.…”

Nonassociativity, Dirac Monopole and Aharonov–bohm Effect

“…a In [28,29], we have used h κ n = κhn + (1 − κ)h −n . One should make substitution κ → (1 + κ)/2 to obtain Eq.…”

“…Nevertheless, the self-consistent theory of Dirac's monopole with an arbitrary magnetic charge can be constructed by using nonassociative structures such as quasigroups and loops. To this end, one needs to consider the nonassociative generalization of the Hopf bundle, employing nonassociative fibre bundle theory [25][26][27][28]. In the context of the group theory, one has to involve infinite-dimensional representations of the rotation group to provide a consistent description of nonquantized Dirac monopole [28][29][30].…”

Smooth Loops and Fiber Bundles: Theory of Principal Q-Bundles

“…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].…”