|Title:||The Mathematical Basis of Gauge Theories of the Yang- Mills Type and Dirac Monopoles|
|???metadata.dc.contributor.*???:||Dr. M. Daniel|
Dr. A. Popovich
|Publisher:||Addis Ababa University|
|Abstract:||After a geometric and intuitive introduction to trivial fiber bundled, a precise presentation of Principal fiber bundles with Lie group structure is given the methods of differential geometry are set up. It is shown how a gauge potential - can be regarded as a connection in some fiber bundle, and the corresponding gauge field as the associated curvature. As an example of a physical case which leads to the Consideration of non-trivial bundles, the magnetic monopole is introduced in its Dirac form together With some notions of duality symmetry (self-dual fields) Monopoles in recent Wu-Yang formulation, and electrodynamics with, monopoles identified i with non-trivial U(l) bundles are studied. The Yang-Mills action functional is defined. The Yang-Mills field equations are derived in terms of the field (curvature). The dual symmetric counterparts of the field equations are established as a consequence of the Bianchi identity of differential geometry. It is shown how the global aspects of the theory (finiteness of the action and the boundary conditions on the gauge potentials) are encoded in the structure of a bundle. The asymptotically vanishing gauge potentials (or pure gauges) are classified using the notions of instanton number and homotopy.|
|Description:||A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of M.Sc in Theoretical Physics and Applied Mathematics by Instructional Course.|
|Appears in Collections:||Thesis - Physics|
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