## PHY 410: Quantum Field Theory I

3 credits | Prerequisites: PHY 307

### Course rationale

Quantum Field Theory (QFT) is the framework where Quantum Mechanics and the Theory of Relativity have been reconciled. This is the description of the microscopic world. The merge of Electrodynamics and QFT begets Quantum Electrodynamics (QED). It can be said that QED is one of the most successful theories. In this first course of QFT, the focus will be on QED and its application to some elementary processes.

### Course content

Review of Classical Field Theory: the field viewpoint, Lagrangian and Hamiltonian description of classical field theory, concept of symmetry, Noether theorem, conserved current; The Klein-Gordon Field: review of notation of special relativity, Klein-Gordon field as harmonic oscillator, Klein-Gordon field in spacetime, canonical quantization, causality and propagators; The Dirac Field: Poincare algebra, Lorentz invariance of Dirac equation, free particle solution of Dirac equation, Dirac matrices, Grassmann numbers, canonical quantization, spin, Dirac, Weyl and Majorana spinors, discrete symmetries: parity, time-reversal, charge conjugation, CPT theorem; Maxwell Field: unitary representation of Poincare group, electromagnetism as gauge theory, gauge covariant derivatives, photon propagator, different gauges; Interacting Fields and Feynman Diagrams: perturbation theory, perturbation expansion of correlation functions, Wick’s theorem, Feynman diagram, Cross Section and S-matrix, quantum electrodynamics, LSZ reduction formula; Elementary Processes of Quantum Electrodynamics: electron-electron to muon-muon scattering, helicity structure, crossing symmetry, nonrelativistic limit; Radiative Corrections: infrared divergences, regularization, Ward-Takahashi Identity, optical theorem.

### Course objectives

- Understand various concepts related to quantum mechanics and relativity.
- Use second quantization to quantize quantum fields.
- Understand the concept of spin.
- Familiarize with anti-commutating Gassmann numbers and fields.
- Familiarize with perturbation theory and Feynman diagrams.
- Calculate different quantities for elementary processes using appropriate Feynman diagrams.
- Understand the divergences coming from loop integrals and the necessity for renormalization.

### References

- An Introduction to Quantum Field Theory (3rd edition) by Michael E. Peskin, Daniel V. Schroeder
- Quantum Field Theory and the Standard Model (1st edition) by Matthew D. Schwartz
- The Quantum theory of fields. Vol. 1: Foundations by Steven Weinberg
- Quantum Field Theory (2nd edition) by Lewis H. Ryder
- Quantum Field Theory by Ulrich M. Srednicki