On representations of the rotation group and magnetic monopoles

Abstract

Recently (Phys. Lett. A302 (2002) 253, hep-th/0208210; hep-th/0403146) employing bounded infinite-dimensional representations of the rotation group we have argued that one can obtain the consistent monopole theory with generalized Dirac quantization condition, 2κµ ∈ Z, where κ is the weight of the Dirac string. Here we extend this proof to the unbounded infinite-dimensional representations.

Can Magnetic Monopoles and Massive Photons Coexist in the Framework of the Same Classical Theory?

“…These conclusions are formulated in a quantum framework which is a quantized version of the classical one. The Hamiltonian formulation and the problems involved in quantization of Dirac's theory of monopoles have been extensively discussed in the past and is still an active field of research [7,8]. Major work on the quantum field theory of magnetic charges has been developed by Schwinger [9,10,11] and Zwanziger [12].…”

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

“…and vice versa. Besides, an arbitrary transformation of the strings S κ n → S κ ′ n ′ can be realized as combination S κ n → S κ n ′ and S κ n → S κ ′ n , where the first transformation preserving the weight of the string is rotation, and the second one results in changing of the weight string κ → κ ′ without changing its orientation [21,52].…”

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.…”

“…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].…”