Entry requirements

120 credits including Quantum Mechanics, Advanced Course.

Learning outcomes

After finishing the course the student should be able to

• explain the physical concept of quantum fields and its manifold interrelations to the concepts of special relativity, symmetries and conservation laws,
• relate the concept and formalism of perturbation theory to the skill of drawing pertinent Feynman diagrams,
• translate Feynman diagrams into mathematical formulae of scattering amplitudes and cross sections for the interactions between microscopic particles,
• generalise the language of Feynman diagrams to new theories, i.e. develop new Feynman rules,
• make use of the mathematical tool of functional integrals,
• contrast measurable and theory intrinsic quantities in the framework of renormalisation theory,
• describe the basic aspects of the connection between the renormalisation framework and a possible more microscopic theory beyond quantum fields,
• plan, carry out and document in the framework of the homework assignments complex mathematical calculations and the solutions of physical problems integrating the achieved understanding and information obtained from the lectures, from textbooks and from exploring other sources based on own initiative,
• discuss and explain the solutions of physical and mathematical problems during lectures and problem-solving sessions.

Content

The whys and hows of quantum field theory. The reasons for the development of quantum field theory in a conceptual and a history of science context and possible limitations of a quantum field theoretical description. The formalism of quantum field theory, in particular: field quantisation; field-theoretical description of identical particles; Klein-­Gordon equation; Lagrange formalism for fields; symmetries, Noether's theorem and conservation laws; Poincare invariance and related discrete symmetries; Lorentz group and its representations; Dirac and Majorana fields; path integrals (functional integrals); scattering theory; perturbation theory and Feynman diagrams; introduction to the concept of renormalisation. The course provides the necessary mathematical and theoretical background for problems in current research of nuclear and particle physics. It also provides a basic working knowledge for the mathematical tool of functional integrals, which are used in wide areas of modern science ranging from particle physics to mathematical finance.

Instruction

Lectures, problem-solving sessions and homework assignments with feedback.

Assessment

Hand­-in problems during the course. To pass the course requires also active participation in the lectures and problem ­solving sessions.