Advanced Quantum Field Theory (PHYC90057)

Quantum field theory has been at the forefront of important breakthroughs in both physics and mathematics in past decades. This subject develops an advanced understanding of the quantum properties of non-Abelian gauge theory via the use of modern field-theoretical methods. Non-Abelian gauge theory is the underlying structure behind the Standard Model of particle physics.

The subject introduces path integrals (including for fermions) in field theory. We develop functional methods to derive Feynman rules from the path integral and calculate the effective action and effective potential. Another major topic is renormalisation. We will explore renormalisation using the method of dimensional regularisation to calculate loop integrals. We will derive the Callan-Symanzik equation and the implications of renormalisation group flow such as asymptotic freedom. We will also study the subtleties of quantising non-Abelian gauge theories through topics such as gauge fixing, Fadeev-Popov ghosts and BRST invariance.

Time permitting, further specific topics may be taken from effective field theory and power-counting, anomalies, non-perturbative techniques, topological defects, and other extended objects in field theory.