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Advanced Quantum Field Theory

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Author(s): D. B. Skinner, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part III Lecture Notes
Publisher: University of Cambridge
Year: 2017

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; quantum mechanics; quantum mechanics; physics; quantum field theory; atomic; nuclear

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