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Quantum Field Theory

Combining special relativity with quantum mechanics led to the discovery of quantum field theory, which is needed to describe matter and its interactions at the most fundamental level. In this course you will learn how particles are field quanta and how the electromagnetic, weak and strong forces arise from symmetries and symmetry breaking.

In this course, you will learn that all matter and its interactions can be described in terms of quantum fields. In particular you learn about the theories of quantum electrodynamics, chromodynamics (strong interactions) and the electroweak theory. You will also learn how to calculate scattering amplitudes and cross sections.

The course begins with an introduction to the classical theory of fields in the Lagrangian and Hamiltonian formulations, and explores the fundamental relation between symmetries and conservation laws, as encoded in Noether's theorem. The quantum theory of fields is then developed, first, for non-interacting scalar fields, the Maxwell field and the Dirac field, clarifying the connection between quantum fields and elementary particles like photons and electrons. Then, to deal with interacting fields, the concepts of S-matrix expansion, scattering amplitudes and cross-sections, Feynman diagrams and rules, etc, are introduced and developed. Local gauge symmetry is introduced as the origin of all known interactions in nature. This directly leads to the theories of the electromagnetic force (quantum electrodynamics) and the strong nuclear force (quantum chromodynamics). To extend it to the weak force, we introduce spontaneous symmetry breaking and the Higgs mechanism as well as Yukawa couplings, and then formulate the unified
electroweak theory as an SU(2)xU(1) gauge theory. Finally, we introduce path integrals (or functional integrals) as an alternative formulation of quantum field theory.

Quantum field theory is used in many branches of physics. Hence, the course is recommended for master students who plan to pursue their studies in any branch of theoretical physics as well as students who plan to study experimental particles physics. The course is also recommended for PhD students in these areas who have not taken an equivalent course in their earlier studies.

Teaching during the autumn term 2020

During the autumn semester 2020, lectures and tutorials will be done remotely through Zoom. The teaching format of the course might be updated for the spring semester. The course is examined through written reports of home work problems and a final remote written exam. The course is using the webpage http://staff.fysik.su.se/~fawad/QFT/

  • Course structure

    This is a second cycle course given at half speed during daytime.  This course can also be taken as a third cycle course.

    More detailed information about the topics covered during this course can be found at the course webpage: Quantum Field Theory

    Teaching format

    The teaching consists of lectures and problem solving sessions.

    Assessment

    The examination on this course consists of two parts:

    Exam: A written examination at the end of the course.
    Homework problems: Written homework problems throughout the course.

    Examiner

    Fawad Hassan

    Phone: +468 5537 8739

    E-mail: fawad@fysik.su.se

  • Schedule

    The schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course.
  • Course literature

    Note that the course literature can be changed up to two months before the start of the course.
    • F. Mandl och G. Shaw, Quantum Field Theory (2nd Edition)
    • Classical Mechanics by H. Goldstein, C. P. Poole, J. L. Safko (chapter 13)
  • Course reports

    Här ligger ett skript.

  • More information

    When can I apply?

    Registration is open from mid-March to mid-April for courses that run in the fall, and from mid-September to mid-October for courses that run in the spring.

    Please note that many courses open for late registration in mid-July for courses in the autumn term and in mid-December for courses in the spring term.

    Read our step by step guide on how to apply

  • Contact

    Course coordinator and teacher:
    Fawad Hassan, tel: 08 5537 8739, e-mail: fawad@fysik.su.se

    Exercises:
    Jorge Laraña Aragon, e-mail: jorge.laranaaragon@fysik.su.se
    Joakim Flinckman, e-mail: joakim.flinckman@fysik.su.se

     

    Academic advisor at the Department of Physics: studievagledare@fysik.su.se

    Student office: studentexp@fysik.su.se