Advanced Quantum Field Theory

Introduction
	What is quantum field theory
	Building a quantum field theory
QFT in zero dimensions
	Free theories
	Interacting theories
	Feynman diagrams
	An effective theory
	Fermions
QFT in one dimension (i.e. QM)
	Quantum mechanics
	Feynman rules
	Effective quantum field theory
	Quantum gravity in one dimension
Symmetries of the path integral
	Ward identities
	The Ward–Takahashi identity
Wilsonian renormalization
	Background setting
	Integrating out modes
	Correlation functions and anomalous dimensions
	Renormalization group flow
	Taking the continuum limit
	Calculating RG evolution
Perturbative renormalization
	Cutoff regularization
	Dimensional regularization
	Renormalization of the phi4 coupling
	Renormalization of QED
Non-abelian gauge theory
	Bundles, connections and curvature
	Yang–Mills theory
	Quantum Yang–Mills theory
	Faddeev–Popov ghosts
	BRST symmetry and cohomology
	Feynman rules for Yang–Mills
	Renormalization of Yang–Mills theory
Index