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Quantum Field Theory

  • 15 credits

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.

  • 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.

    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, and
    Homework problems: Written homework problems throughout the course.

    Examiner

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

    Lectures:
    Fawad Hassan, tel: 08 5537 8739, e-mail: fawad@fysik.su.se

    Problem solving sessions:
    Francesco Torsello,  e-mail: francesco.torsello@fysik.su.se
    Julius Engelsöy, e-mail: julius.engelsoy@fysik.su.se
    Jorge Laraña Aragon, e-mail: jorge.laranaaragon@fysik.su.se

     

  • Schedule

    This is a preliminary schedule and is subject to continuous change. For this reason, we do not recommend print-outs. At the start of the course, your institution will advise where you can find your schedule during the course.

    Schedule FK8027 Autumn 2019 - Spring 2020

  • 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)
  • Contact

    Academic Advisor

    studievagledare@fysik.su.se

     

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