After completing the course, the student should acquire basic knowledge of some advanced topics in Mathematical Physics, such as the elements of functional analysis, the elements of algebra and group theory and the elements of differential geometry. The student should be able to solve problems within these topics and describe their significance in modern physics.
The course is the direct continuation of the course in Mathematical methods of Physics (1FA121). The course deals with advanced topics in mathematical physics: the elements of functional analysis (topological space, metric space, Hilbert space, self-adjoint operators and their application in quantum mechanics), the elements of abstract algebra and group theory (associative, Lie algebra, Lie group, matrix groups, representations), the elements of topology and differential geometry with their application in physics (smooth manifolds, tensors, differential forms, fibre bundles, gauge theory, Yang-Mills theory).
Lectures and lessons.
Examination at the end of the course.
week 32, 2010
Richtmyer, Robert D.
Principles of advanced mathematical physics : Vol. 1