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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TIF310 - Symmetry
Syllabus adopted 2019-02-14 by Head of Programme (or corresponding)
Owner: MPPHS
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: Second-cycle
Major subject: Engineering Physics
Department: 16 - PHYSICS

Teaching language: English
Application code: 85122
Open for exchange students: Yes
Block schedule: A

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0119 Written and oral assignments 7,5 c Grading: TH   7,5 c    

In programs

MPPHS PHYSICS, MSC PROGR, Year 1 (compulsory elective)


Martin Cederwall

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In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Special relativity


The purpose of the course is to give a basic knowledge in classical field theory, with special focus on symmetries, global and local. This provides a preparation for continued studies of e.g. gravity and quantum field theory.

Learning outcomes (after completion of the course the student should be able to)

After completed course, the student is expected to master basic elements of classical, including relativistic, field theory for different kinds of fields. In particular, an understanding of global and local symmetries in field theories is expected. 


Discrete symmetries, CPT;
Continuous symmetries: Lie groups and algebras and their representations;
Rotational symmetries, Lorentz and Poincaré algebras;
Basic classical, incl. relativistic, field theory;
Action principle, Hamiltonian formulation;
Noether's theorem;
Currents and charges, the stress tensor;
Gauge theory: minimal coupling, covariant derivatives, topological properties;
Spinors, the Dirac equation




lecture notes

Examination including compulsory elements

Home assignments

Page manager Published: Thu 04 Feb 2021.