Quantum Field Theory I

About this programme

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.