Mathematical Methods of Physics II
Syllabus, Master's level, 1FA155
- Code
- 1FA155
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Physics A1N
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 19 October 2023
- Responsible department
- Department of Physics and Astronomy
General provisions
This course allows you to delve into advanced mathematical concepts critical in physics. Throughout the course, you will explore topics such as functional analysis, topological spaces, self-adjoint operators in quantum mechanics, abstract algebra and group theory, and differential geometry, with practical applications in physics. The goal is for you to develop the ability to solve complex problems in mathematical physics and understand their relevance in modern physics. This course equips you with the necessary tools to take your mathematical skills to the next level and comprehend how they are crucial to our understanding of the universe.
Entry requirements
120 credits with Mathematical Methods of Physics. Participation in Symmetry and Group theory or the course Algebraic structures is required. Proficiency in English equivalent to the Swedish upper secondary course English 6.
Learning outcomes
On completion of the course, the student should be able to:
- solve problems within advanced topics in Mathematical Physics, such as functional analysis, algebra and group theory, and differential geometry
- account for their importance within modern physics
Content
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).
Instruction
Lectures and lessons.
Assessment
Examination at the end of the course.
If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.