Course syllabus adopted 2024-02-02 by Head of Programme (or corresponding).
Overview
- Swedish nameMatematisk fysik och speciell relativitetsteori
- CodeTIF390
- Credits6 Credits
- OwnerTKTFY
- Education cycleFirst-cycle
- Main field of studyEngineering Physics
- DepartmentPHYSICS
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language Swedish
- Application code 57140
- Block schedule
- Open for exchange studentsNo
- Only students with the course round in the programme overview.
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0123 Examination 6 c Grading: TH | 6 c |
|
In programmes
Examiner
Gabriele Ferretti- Head of Unit, Subatomic, High Energy and Plasma Physics, Physics
Eligibility
General entry requirements for bachelor's level (first cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
The same as for the programme that owns the course.Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
Basic courses on analysis, complex analysis, linear algebra, mechanics and electromagnetism
Aim
Expand the "toolbox" of mathematics to be able to describe and use the symmetries of a physical system using group theory, solve dynamical problems using advanced analytical methods, and solve problems in relativistic physics using tensors.
Learning outcomes (after completion of the course the student should be able to)
Construct a finite group multiplication table.
Decompose the product of two or more irreducible representations of a finite group.
Exponentiate a matrix.
Calculate the sum of two spin operators.
Determine when a Fredholm integral equation has a solution and choose between different solution methods.
Use distributions and Green's function methods to solve problems in the calculus of variations.
Derive Euler's equations using functional derivatives.
Use saddle point methods to calculate the asymptotic value of an integral.
Calculate energy of decay products or threshold energy in simple processes in nuclear/particle physics.
Formulate Maxwell's equations in 4-dimensional tensor form.
Content
1. Group and representation theory:Discrete groups, Permutation group, Orthogonality theorem, Character of a representation, Continuous groups, Lie algebras, SU(N), SO(N), Spin, SU(2) vs SO(3).
Distributions, Green's functions, Analyticity, Integral equations, Functional derivatives, Variational calculus, Saddle point method.
3. Special Relativity:
Einstein's postulate of relativity, Lorentz transformation, 4-dimensional notation, Relativistic mechanics, Tensors,
Maxwell's equations in tensor form.
Organisation
Lectures and exercises.Literature
Only free material from the web will be used in addition to my lecture notes.
Main examples:
Introduktion till speciell relativitetsteori, G. Ferretti et al.
Lie Algebras In Particle Physics from Isospin To Unified Theories, H. Georgi.
Greens functions, integral equations, and calculus of variations, (various authors).
(Links in the course homepage)
Lie Algebras In Particle Physics from Isospin To Unified Theories, H. Georgi.
Greens functions, integral equations, and calculus of variations, (various authors).
(Links in the course homepage)
Examination including compulsory elements
Mandatory assignments and written exam.
Grade scale (exam+assignment): 40% :3 (pass), 60%:4 (pass with credit), 80%:5 (pass with distinction).
The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.