Syllabus for Geometrical Methods in Theoretical Physics

Geometriska metoder i teoretisk fysik

Syllabus

  • 10 credits
  • Course code: 1FA153
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Physics A1F

    Explanation of codes

    The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:

    First cycle
    G1N: has only upper-secondary level entry requirements
    G1F: has less than 60 credits in first-cycle course/s as entry requirements
    G1E: contains specially designed degree project for Higher Education Diploma
    G2F: has at least 60 credits in first-cycle course/s as entry requirements
    G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
    GXX: in-depth level of the course cannot be classified.

    Second cycle
    A1N: has only first-cycle course/s as entry requirements
    A1F: has second-cycle course/s as entry requirements
    A1E: contains degree project for Master of Arts/Master of Science (60 credits)
    A2E: contains degree project for Master of Arts/Master of Science (120 credits)
    AXX: in-depth level of the course cannot be classified.

  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2010-01-28
  • Established by:
  • Revised: 2020-02-10
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 30, 2020
  • Entry requirements: 120 credits including Mathematical Methods of Physics II.
  • Responsible department: Department of Physics and Astronomy

Learning outcomes

On completion of the course, the student should be able to:

  • analyse and solve simple problems in topology (e.g. simple homotopy, homology and cohomology calculations)
  • perform simple manipulations with connections and characteristic classes on fibre bundles.
  • use the geometrical tools that are used widely in modern quantum feld theory and string theory
  • account for the geometrical notions behind the description of gauge theories
  • discuss applications of topology in various physical problems

Content

Topology, smooth manifolds, Lie groups, homotopy, homology, cohomology, principal and vector bundles, connections on fibre bundles, characteristic classes and their application in physics, Yang-Mills theory and more advanced topics based on students' interests.

Instruction

Lectures and classes ("flipped classroom" might be used).

Assessment

Hand-in problems during 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.

Other directives

The course is given in coordination with the third-cycle programmes.

Reading list

Reading list

Applies from: week 02, 2020