Course Syllabus

Quantum Field Theory in Curved Space

PHY7097-1535(16421)

Class Periods: MWF Period 3 (9:35-10:25am)

Location: NPB 1200

Academic Term: Fall 2025

Instructor:

• Richard Woodard, NPB 2065
  
• woodard@phys.ufl.edu
• +1-352-392-8744
• Office Hours: W5 (11:45-12:35pm) and R10 (5:10-6:00pm)

Course Description: PHY7097 Quantum Field Theory in Curved Space, 3 Credits, Letter Grade

Special studies in mathematical methods and applications of current interest at the forefront of one or more specialties in theoretical physics.

Course Prerequisites

There are no prerequisites, and the course will be self-contained, but familiarity with certain material from the following courses would be useful:

• PHY6648 - Quantum Field Theory 1
• PHZ6607 - General Relativity 1

Course Objectives

This is an advanced graduate course on quantum field theory techniques for primordial inflation. Specific objectives of this semester are:

• FLRW Cosmology.
• The Lambda CDM Model.
• Scalar-driven inflation.
• QFT in position space.
• The gauge of Bardeen, Bond and Salopek.
• The primordial power spectra.
• Non-Gaussianity.
• The functional formalism.
• The Schwinger-Keldysh formalism.
• How 1PI functions quantum-correct classical field equations.
  
• How to use dimensional regularization in position space.
  

Required Text

• Inflationary Cosmology: Lecture Notes in Physics 738
• Edited by M. Lemoine, J. Martin and P. Peter
• Springer, Heidelberg, 2008
• ISBN 978-3-540-74352-1

Course Schedule

• Day 1 (Aug. 22) FLRW Cosmology.
• Day 2 (Aug. 25) The Lambda CDM Model.
  
• Day 3 (Aug. 27)  Scalar-driven inflation: how-to do it.
• Day 4 (Aug. 28) Why inflation is necessary. (MAKEUP CLASS) 
• Homework #1 due by 9:35am on Aug. 29
• Day 5 (Aug. 29) Overview of general relativity.
  
• Labor Day Holiday (Sept. 1)
• No Class (Sept. 3)
• No Class (Sept. 5)
• Day 6 (Sept. 8) The massless, minimally coupled scalar on FLRW. 
  
• Day 7 (Sept. 10) Solving the mode equation.
• Homework #2 due by 9:35am on Sept. 12
• Day 8 (Sept. 12) Coulomb gauge versus Feynman gauge in flat space QED.
  
• Day 9 (Sept. 15) The gauge of Bardeen, Bond and Salopek.
  
• Day 10 (Sept. 17) The primordial power spectra.
• Day 11 (Sept. 18) Non-Gaussianity.  (MAKEUP CLASS) 
• Homework #3 due by 9:35am on Sept. 19
• Day 12 (Sept. 19) The in-out formalism of QFT versus the in-in formalism.
• Day 13 (Sept. 22) The functional formalism.
  
• Day 14 (Sept. 24) Schwinger-Keldysh formalism in flat space.
  
• Homework #4 due by 9:35am on Sept. 26
• Day 15 (Sept. 26) Veneziano's model.
• Day 16 (Sept. 29)  Dimensional regularization in position space.
  
• Day 17 (Oct. 1) Renormalization in position space.
• Homework #5 due by 9:35am on Oct. 3
• Day 18 (Oct. 3) Propagators on de Sitter background.
• Day 19 (Oct. 6) Massless, minimally coupled scalar with a quartic self-interaction.
  
• Day 20 (Oct. 8) The VEV of the scalar stress tensor at 2-loop order.
• Homework #6 due by 9:35am on Oct. 10
• Day 21 (Oct. 10) Initial state corrections.
• Day 22 (Oct. 13) The leading logarithm approximation.
  
• Day 23 (Oct. 15) Starobinsky's stochastic formalism for scalar potential models.
• Homework #7 due by 5:10pm on Oct. 16
• Day 24 (Oct. 16)  (MAKEUP CLASS) Taking the late time limit.
• UF Homecoming (Oct. 17)
• Day 25 (Oct. 20) 1PI n-point functions.
• Day 26 (Oct. 22) The scalar self-mass at 2-loop order.
• Homework #8 due by 9:35am on Oct. 24 
  
• Day 27 (Oct. 24) The effective field equations.
• Day 28 (Oct. 27) Solving for the scalar mode function. 
  
• Day 29 (Oct. 29) The vacuum polarization from SQED.
• Homework #9 due by 9:35am on Oct. 31
  
• Day 30 (Oct. 31) Solving for the photon mode function.
• Day 31 (Nov. 3) Solving for the Coulomb potential.
  
• Day 32 (Nov. 5) Nonlinear sigma models.
• Homework #10 due by 9:35am on Nov. 7
• Day 33 (Nov. 7) Renormalization group logarithms.
• Day 34 (Nov. 10) Approximating propagators for FLRW.
• Day 35 (Nov. 12) Weinberg's version of the SK formalism.
• Day 36 (Nov. 13) (MAKEUP CLASS)
• Homework #11 due by 9:35am on Nov. 14
• Day 37 (Nov. 14) Inflationary correlators.
• Day 38 (Nov. 17) Features.
• Day 39 (Nov. 19) Different vacua.
• Homework #12 due by 9:35am on Nov. 21
• Day 40 (Nov. 21) Open problems.
• 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