Quantum Field Theory I

Course description

First semester of a 2-semester basic course on quantum field theory. The course subjects include:

Part I: QFT of the scalar field

• path integral quantization of the free scalar field
• continuous spacetime symmetries in classical field theories
• Feynman diagrams and Feynman rules for scalar phi^4 theory
• canonical quantization of the scalar field
• continuous symmetries in QFT
• internal symmetries
• discrete symmetries
• spontaneous symmetry breaking
• a first look at renormalization
• the large-N expansion

Part II: QFT of the fermion field

• representations of the Lorentz group
• the Dirac Lagrangian and equation
• the Clifford algebra and the gamma matrices 
• canonical quantization for spinors
• the fermionic path integral
• Feynman rules for fermions

The exercise sessions and exercise sheets are integral part of the course, as some essential concepts are developed there!

This course should be attended in parallel with "Exercices in Theoretical Physics" and before "Quantum Field Theory II" (Spring semester).

Literature:

My notes are largely based on:

• A. Zee, Quantum field theory in a nutshell, Princeton University Press, 2003
• S. Coleman, Quantum Field Theory Lectures, World Scientific, 2019

Additional reading:

• E. Fradkin, Quantum Field Theory - an integrated approach, Princeton University Press 2021
• M.E. Peskin, D.V. Schroeder, An introduction to quantum field theory, Addison-Wesley, 1995