Course Syllabus

Quantum Field Theory 1

PHY6648-68E3(18449)

Class Periods: MWF Period 8 (3:00-3:50pm)

Location: NPB 1200

Academic Term: Fall 2025

Instructor:

• Richard Woodard, NPB 2065
  
• woodard@phys.ufl.edu
• +1-352-392-8744
• Office Hours: W6 (12:50-1:40pm) and R9 (4:05-4:55pm)

Course Description: PHY6648 Quantum Field Theory 1, 3 Credits, Letter Grade

The Poincare group; the Dirac equation; quantization of free fields; the scattering matrix; applications.

Course Prerequisites

• PHY6346 and PHY6347 - Graduate Electrodynamics
• PHY6246 - Graduate Classical Mechanics

Course Objectives

This is the first semester of a 3-part course whose purpose is to prepare students for advanced research in high energy particle theory and condensed matter theory. Specific objectives of this semester are:

• The Heisenberg picture of Quantum Mechanics.
  
• The Poincare group and its representations for spin (or helicity) 0, 1/2 and 1. 
• Free fields for spin 0, 1/2 and 1, including operators expansions and propagators.
  
• How to read off the Feynman rules from a Lagrangian.
  
• How to compute invariant amplitudes.
  
• How to turn invariant amplitudes into rates and cross sections, including spin a polarization sums.
  
• Classic tree amplitudes in QED, including Compton scattering and Bhabha scattering.
  
• Classic 1-loop 1PI functions in dimensionally regulated QED, including the electron self-energy, the vacuum polarization and the vertex function, which gives g-2.
  
• On-shell renormalization.

Required Text

• An Introduction to Quantum Field Theory
• by Daniel V. Schroeder and Michael E. Peskin
• 1995
• ISBN 9780201503975, 9780429503559 (eBook), 9780429494178

Course Schedule

• Day 1 (Aug. 22) Introductory comments.
  
• Day 2 (Aug. 25) Heisenberg picture.
  
• Day 3 (Aug. 27) Heisenberg picture. 
• Day 4 (Aug. 28) Complex scalar field. (MAKEUP CLASS)
• Homework #1 due by 3pm on Aug. 29
• Day 5 (Aug. 29) Noether's Theorem
  
• Labor Day Holiday (Sept. 1)
• No Class (Sept. 3)
• No Class Holiday (Sept. 5)
• Day 6 (Sept. 8) Source-free electromagnetism.
  
• Day 7 (Sept. 10) Polarization vectors and SQED.
• Homework #2 due by 3pm on Sept. 12
• Day 8 (Sept. 12) Feynman gauge.
  
• Day 9 (Sept. 15) Poincare group.
  
• Day 10 (Sept. 17)  Spinor representations of the Lorentz group.
• Day 11 (Sept. 18) Gamma matrix algebra. (MAKEUP CLASS)
• Homework #3 due by 3pm on Sept. 19
• Day 12 (Sept. 19) Initial value solution of the Dirac equation.
• Day 13 (Sept. 22) The need for anti-commutation relations.
  
• Day 14 (Sept. 24) Spinor wave functions.
  
• Homework #4 due by 3pm on Sept. 26
• Day 15 (Sept. 26) Dirac spin sums & the Dirac propagator.
• Day 16 (Sept. 29) Gamma matrix algebra. 
  
• Day 17 (Oct. 1) Nonrelativistic limit of QED.
• Homework #5 due by 3pm on Oct. 3
• Day 18 (Oct. 3) Disconnected parts of the Lorentz Group.
• Day 19 (Oct. 6) The easy way to get propagators.
  
• Day 20 (Oct. 8) The Interaction Picture.
• Homework #6 due by 3pm on Oct. 10
• Day 21 (Oct. 10) The Invariant Amplitude and what to do with it.
• Day 22 (Oct. 13) Bhabha Scattering.
  
• Day 23 (Oct. 15) Feynman rules for QED.
• Homework #7 due by 4:05pm on Oct. 16
• Day 24 (Oct. 16) Feynman rules generally and differential cross sections. (MAKEUP CLASS)
• UF Homecoming (Oct. 17)
• Day 25 (Oct. 20) QED in Coulomb gauge & the nonlinear pendulum.
• Day 26 (Oct. 22) Mandelstam parameters & deriving the S-matrix.
• Homework #8 due by 3pm on Oct. 24 
  
• Day 27 (Oct. 24) Complete deriving the S-matrix & spin sums.
• Day 28 (Oct. 27) Review of the Feynman rules.
  
• Day 29 (Oct. 29) Compton scattering.
• Homework #9 due by 3pm on Oct. 31
  
• Day 30 (Oct. 31) Green's functions, 1PI functions & symmetry factors. 
  
• Day 31 (Nov. 3) Loops in dimensional regularization.
  
• Day 32 (Nov. 5) On-shell renormalization in scalar field theory.
• Homework #10 due by 3pm on Nov. 7
• Day 33 (Nov. 7) Perturbation theory generally.
• Day 34 (Nov. 10) On-shell renormalization in SQED.
• Day 35 (Nov. 12) On-shell renormalization in QED.
• Day 36 (Nov. 13) (MAKEUP CLASS)
• Homework #11 due by 3pm on Nov. 14
• Day 37 (Nov. 14) The electron self-energy in QED.
• Day 38 (Nov. 17) The vacuum polarization in QED.
  
• Day 39 (Nov. 19) The vertex function in QED.
• Homework #12 due by 3pm on Nov. 21
• Day 40 (Nov. 21) The gyromagnetic ratio of the electron.
• Thanksgiving Holiday Recess (Nov. 24)
• Thanksgiving Holiday Recess (Nov. 26)
  
• Thanksgiving Holiday Recess (Nov. 28)
• No class (Dec. 1)
• No class (Dec. 3)

Attendance Policy, Class Expectations, and Make-Up Policy

Students are expected to attend lectures but attendance will not be taken, nor is there any penalty for absence. Class notes will be posted under ``Files''. Homework will be assigned weekly, due at the start of class on Fridays and returned in class on Mondays. Excusing missed assignments must be consistent with university policies in the Graduate Catalog (Link) and will require appropriate documentation.

Evaluation of Grades 

There will be no exams. The course grade will be based entirely on 12 weekly homework assignments, worth 15 points apiece.

Grading Policy (Grade cutoffs may be lowered but they will not be raised)

UF Policies

This course complies with all UF policies. For information on those policies and for a list of campus resources, please see this page: https://go.ufl.edu/syllabuspolicies .

Software Use

All faculty, staff, and students of the University are required and expected to obey the laws and legal agreements governing software use. Failure to do so can lead to monetary damages and/or criminal penalties for the individual violator. Because such violations are also against University policies and rules, disciplinary action will be taken as appropriate. We, the members of the University of Florida community, pledge to uphold ourselves and our peers to the highest standard of honesty and integrity