Course Syllabus

Quantum Field Theory 1

PHY6648-68E3(21826)

Class Periods: MWF Period 10 (5:10-6:00pm)

Location: NPB 1002

Academic Term: Fall 2023

Instructor:

  • Richard Woodard, NPB 2065
  • woodard@phys.ufl.edu
  • +1-352-392-8744
  • Office Hours: T6 (12:50-1:40pm) and W5 (11:45-12:35pm)

Canvas Information

Canvas is the where course content, grades, and communication will reside for this course.

  • ufl.instructure.com
  • For Canvas, Passwords, or any other computer-related technical support contact the IT Service Desk.
    • 123 123-1234
    • 877 878-8325
    • http://it.myinstitution.edu
    • itsupport@myinstitution.edu

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

  • Quantum Field Theory and the Standard Model
  • Mathhew D. Schwartz
  • 2014
  • ISBN 9781107034730

Course Schedule

  • Day 1 (Aug. 23) Introductory comments.
  • Day 2 (Aug. 25) Heisenberg picture.
  • Day 3 (Aug. 28) Heisenberg picture.
  • Homework #1 due by 5:10pm on Aug. 30
  • Day 4 (Aug. 30) Hurricane Idalia!
  • Day 5 (Sept. 1) Complex scalar field.
  • Labor Day Holiday (Sept. 4)
  • Homework #2 due by 5:10pm on Sept. 6
  • Day 6 (Sept. 6) Noether's Theorem.
  • Day 7 (Sept. 8) Noether currents for a free complex scalar.
  • Day 8 (Sept. 11) Source-free electromagnetism.
  • Homework #3 due by 5:10pm on Sept. 13
  • Day 9 (Sept. 13) Polarization vectors and SQED.
  • Day 10 (Sept. 15) Feynman gauge.
  • Day 11 (Sept. 18) Poincare group.
  • Homework #4 due by 5:10pm on Sept. 20
  • Day 12 (Sept. 20) Spinor representations of the Lorentz group.
  • Day 13 (Sept. 22) Gamma matrix algebra.
  • Day 14 (Sept. 25) Initial value solution of the Dirac equation.
  • Homework #5 due by 5:10pm on Sept. 27
  • Day 15 (Sept. 27) The need for anti-commutation relations.
  • Day 16 (Sept. 29) Spinor wave functions.
  • Day 17 (Oct. 2) Dirac spin sums & the Dirac propagator.
  • Homework #6 due by 5:10pm on Oct. 4
  • Day 18 (Oct. 4) Gamma matrix algebra.
  • UF Homecoming Holiday (Oct. 6)
  • Day 19 (Oct. 9) Nonrelativistic limit of QED.
  • Homework #7 due by 5:10pm on Oct. 11
  • Day 20 (Oct. 11) Disconnected parts of the Lorentz Group.
  • Day 21 (Oct. 13) The easy way to get propagators.
  • Day 22 (Oct. 16) The Interaction Picture.
  • Homework #8 due by 5:10pm on Oct. 18
  • Day 23 (Oct. 18) The Invariant Amplitude and what to do with it.
  • Day 24 (Oct. 20) Bhabha Scattering.
  • Day 25 (Oct. 23) Feynman rules for QED.
  • Homework #9 due by 5:10pm on Oct. 25
  • Day 26 (Oct. 25) Feynman rules generally and differential cross sections.
  • Day 27 (Oct. 27) QED in Coulomb gauge & the nonlinear pendulum.
  • Day 28 (Oct. 30) Mandelstam parameters & deriving the S-matrix.
  • Homework #10 due by 5:10pm on Nov. 1
  • Day 29 (Nov. 1) Review of the Feynman rules.
  • Day 30 (Nov. 3) Complete deriving the S-matrix & spin sums.
  • Day 31 (Nov. 6) Compton scattering..
  • Homework #11 due by 5:10pm on Nov. 8
  • Day 32 (Nov. 8) Green's functions, 1PI functions & symmetry factors.
  • Veteran's Day Holiday Recess (Nov. 10)
  • Day 33 (Nov. 13) Loops in dimensional regularization.
  • Homework #12 due by 5:10pm on Nov. 15
  • Day 34 (Nov. 15) On-shell renormalization in scalar field theory.
  • Day 35 (Nov. 17) Perturbation theory generally.
  • Day 36 (Nov. 20) On-shell renormalization in SQED.
  • Thanksgiving Holiday Recess (Nov. 22)
  • Thanksgiving Holiday Recess (Nov. 24)
  • Day 37 (Nov. 27) On-shell renormalization in QED.
  • Homework #13 due by 5:10pm on Nov. 29
  • Day 38 (Nov. 29) The electron self-energy in QED.
  • Day 39 (Dec. 1) The vacuum polarization in QED.
  • Day 40 (Dec. 4) The vertex function in QED.
  • Homework #14 due by 5:10pm on Dec. 6
  • Day 41 (Dec. 6) g-2.

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 Wednesdays and returned in class on Fridays. 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 14 weekly homework assignments, worth 15 points apiece.

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

Percent Points
 		Grade Grade Points
85 - 100 178.5 - 210.0 A 4.00
80 - 85 168.0 - 178.5 A- 3.67
75 - 80 157.5 - 168.0 B+ 3.33
70 - 75 147.0 - 157.5 B 3.00
65 - 70 136.5 - 147.0 B- 2.67
60 - 65 126.0 - 136.5 C+ 2.33
55 - 60 115.5 - 126.0 C 2.00
50 - 55 105.0 - 115.5 C- 1.67
45 - 50 94.5 - 105.0 D+ 1.33
40 - 45 84.0 - 94.5 D 1.00
35 - 40 73.5 - 84.0 D- 0.67
  0 - 35      0 - 73.5 E 0.00

Students Requiring Accommodations

Students with disabilities who experience learning barriers and would like to request academic accommodations should connect with the disability Resource Center by visiting Link . It is important for students to share their accommodation letter with their instructor and discuss their access needs, as early as possible in the semester.

Course Evaluation

Students are expected to provide feedback on the quality of instruction in this course by completing online evaluations at Link . Evaluations are typically open during the last two or three weeks of the semester, but students will be given specific times when they are open. Summary results of these assessments are available to students at Link .

University Honesty Policy

UF students are bound by The Honor Pledge which states, ``We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honor and integrity by abiding by the Honor Code. On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: ``On my honor, I have neither given nor received unauthorized aid in doing this assignment.'' The Honor Code (Link) specifies a number of behaviors that are in violation of this code and the possible sanctions. Furthermore, you are obligated to report any condition that facilitates academic misconduct to appropriate personnel. If you have any questions or concerns, please consult with the instructor.

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.

Student Privacy

As in all courses, unauthorized recording and unauthorized sharing of recorded materials is prohibited. Also, there are federal laws protecting your privacy with regards to grades earned in courses and on individual assignments. For more information, please see Link .

Health and Wellness

  • U Matter, We Care: If you or a friend is in distress, please contact umatter@ufl.edu or 352 392-1575 so that a team member can reach out to the student.
  • Counseling and Wellness Center: http://www.counseling.ufl.edu/cwc, and  392-1575; and the University Police Department: 392-1111 or 9-1-1 for emergencies.
  • Sexual Assault Recovery Services (SARS) Student Health Care Center, 392-1161.
  • University Police Department at 392-1111 (or 9-1-1 for emergencies), or http://www.police.ufl.edu/.

Academic Resources