The Mathematical Basis Gauge Theories of The Yang-Mills type and Dirac Monopoles

No Thumbnail Available



Journal Title

Journal ISSN

Volume Title


Addis Ababa University


l\fter? g90metric and intuitive introduction to ~~n-trivial fibe~ bundleJ~ a precise presentation of principal fiber bundles ~ith Lie group structure is given. The methods of differential geometry are set up. It is , 'I ,,' I shown how a gauge potent~alcan be regarded as a connection in some fiber' bundle" an1 the corresponding gauge field as,the associated curvat~re. l\s an example of a physical case which l,,'ads to the 'Jon[;ide~ati.on of' bundles I th~magne~i~ monoPol~ is! introduced in its Dirac form together 'I ' \,;;lth some notiol;ts of du~tity symmetry (self dual fields). 'I ' t1onopoles 'in t~e recent \~u-Yang formulation I and electrodynamicswit~ mohbpoles identified with non-trivial , i U(l) bundles are studiedl The yang-~lills action functional , , :is, def ined. : I I 'of the -'.-;' of the of the " ,The i Y~ng-Millsl field equation are derived in terms . I ,fielo (curvature) i. , , i The dual synunetric counterparts " I field e~uations a~e , I established as a consequence ~ianchi identitY~f differential geometry. It is , S'hO\'ll) hovi the global asp'ects of, the theory (f ini teness of the action and the boundary conditions on the gauge p~tentials) ~re;encoded lin the structure of a bundle. The . ' I asymptotically vanishing; gauge potentials (or pure gauges) ~;e classified usi,ng th I notions of instantoI,l number and homotopy



The Mathematical Basis Gauge Theories