After passing the course the student should be able to
use the pathintegral formalism to quantize an arbitrary field theory with both bosonic and fermionic fields
derive the Feynman rules for a gauge theory using pathintegrals
derive the Higgs mechanism and spontaneous symmetry breaking
use the renormalisation group and how to regularize in an arbitrary gauge-theory
derive the BRST symmetry and to analyse in examples how it mirrors gauge invariance in the quantum theory
explain the phenomenon of anomalies and to calculate them in a number of examples
explain basic supersymmetry and supersymmetric quantum field theory with applications
analyse the conceptual problems that arise in quantizing gravity.
The course establishes the relation of standard canonical quantisation formalism for field theories to path-integral quantisation. The course will also familiarise the students with some basic concepts in advanced quantum field theory such as path-integral quantisation of gauge theories, regularisation and the renormalisation group, BRST-quantisation, Higgs-mechanism, spontaneous symmetry breaking, anomalies and supersymmetry.
Homework assignments, possibly amended by an oral exam.