In J.D. Jackson's Classical Electrodynamics textbook, the analysis of Dirac's charge quantization condition in the presence of a magnetic monopole has a mathematical omission and an all-too-brief physical argument that might mislead some students. This paper presents a detailed derivation of Jackson's main result, explains the significance of the missing term, and highlights the close connection between Jackson's findings and Dirac's original argument. (C) 2016 Sharif University of Technology. All rights reserved.

This thesis is concerned with the quantum Dirac magnetic monopole and two classes of its generalisations. The first of these are certain analogues of the Dirac magnetic monopole on coadjoint orbits of compact Lie groups, equipped with the normal metric. The original Dirac magnetic monopole on the unit sphere S^2 corresponds to the particular case of the coadjoint orbits of SU(2). The main idea is that the Hilbert space of the problem, which is the space of L^2-sections of a line bundle over the orbit, can be interpreted algebraically as an induced representation. The spectrum of the corresponding Schodinger operator is described explicitly using tools of representation theory, including the Frobenius reciprocity and Kostant's branching formula. In the second part some discrete versions of Dirac magnetic monopoles on S^2 are introduced and studied. The corresponding quantum Hamiltonian is a magnetic Schodinger operator on a regular polyhedral graph. The construction is based on interpreting the vertices of the graph as points of a discrete homogeneous space G/H, where G is a binary polyhedral subgroup of SU(2). The edges are constructed using a specially selected central element from the group algebra, which is used also in the definition of the magnetic Schrodinger operator together with a character of H. The spectrum is computed explicitly using representation theory by interpreting the Hilbert space as an induced representation.

Kaluza-Klein theories generally in $(4+D)$ and more specifically in five dimensions are reviewed. The magnetic monopole solutions found in the Kaluza-Klein theories are generally reviewed and their generalizations to Anti-de Sitter spacetimes are discussed.

No description available.

No description available.