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# Quantum Field Theory I

• 7.5 credits
• Master’s level
• Spring Term 2025

Content
The course begins with an introduction to relativistic quantum mechanics with the Dirac and Klein-Gordon equations. Lagrange formulation of field theories and the relationship between symmetries and conserved quantities are then treated. Thereafter, the scalar, Dirac and photon fields are quantised using canonical quantisation, and annihilation and creation operators as well as the concept of propagator are introduced. Then the S-matrix expansion is studied and the Feynman rules for quantum electrodynamics (QED) are developed. Finally, QED is applied at the lowest order to various scattering processes such as Compton scattering.

Expected study results
To fulfil the goals of knowledge and understanding, the student should be able to:

• understand and be able to explain in detail key concepts such as Klein-Gordon field, Dirac field, photon field, field quantisation, annihilation and creation operators, commutator, propagator and S-matrix
• derive central results such as Noether's theorem, Wick's theorem and the Feynman rules, be able to explain in detail the different steps in the derivations, and be able to explain the meanings of the results in themselves and for the quantum field theory as a whole.

To fulfil the goals for proficiency and ability, the student should be able to:

• independently quantise a classical field theory
• based on the Lagrangian for a field theory, develop corresponding Feynman rules
• treat spin and polarisation sums
• perform complex calculations to determine the lowest order scattering cross section in QED for various physical processes.

To fulfil the goals for values and critical approach, the student should be able to:

• independently and with a critical approach be able to assimilate and evaluate scientific literature in the field.

Eligibility
Previous university studies of at least 90 higher education credits including Quantum Mechanics 2, 7.5 credits, and one of the courses General Theory of Relativity, 7.5 credits, or Electrodynamics II, 7.5 credits, or equivalent.

Forms of instruction
The teaching is conducted in the form of teacher-led seminars where the lectures circulate between the participants. In addition to scheduled activities, individual work with the course material is also required.

Examination
The examination on the course takes place individually in the form of assignments and through lectures given by the student himself. On assignments and lectures, one of the grades Fail (U), Pass (G) or Pass with Distinction (VG) is given.

On the entire course, one of the grades Fail (U), Pass (G) or Pass with Distinction (VG) is given. The grade constitutes a summary assessment of the results in the various parts of the examination and is only set when all parts have been approved. Those who pass an exam may not undergo a re-exam for higher grades.

Literature
Quantum field theory
Mandl F., Shaw G.
2nd ed. : Chichester: Wiley: 2010: xii, 478 p .:
ISBN: 978-0-471-49684-7 (hft.)
See the library's search service

Material provided by the department on relativistic quantum mechanics.

## Application and eligibility

### Quantum Field Theory I, 7.5 credits

Spring Term 2025

20 January 2025

24 March 2025

Umeå

English

Daytime, 50%

#### Required Knowledge

90 credits including Quantum Mechanics 2 and either General Relativity or Electrodynamics II or equivalent. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies. Requirements for Swedish only apply if the course is held in Swedish.

#### Selection

Academic credits Applicants in some programs at Umeå University have guaranteed admission to this course. The number of places for a single course may therefore be limited.

UMU-53126

#### Application

Online applications are now open. You will be transferred to Universityadmissions.se. Application deadline is 15 October 2024. How to apply

#### Application and tuition fees

As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.

SEK 900

SEK 17,850

SEK 17,850