Quantum Field Theory I

Physics 8808.01, Autumn 2012

Office: M2042 Physics Research Bldg

Office Hours: stop by anytime

Course Meets: Tuesdays, Thursdays 11:10 am - 12:30 pm, Scott Lab, room E0245.

Grader: Douglas Wertepny , PRB M2041

*** First Class Meets August 23, 2012 ***

*** There will be no class September 11 (Tuesday) and 13 (Thursday), 2012 - I will be out of town ***

*** There will be a makeup class Wednesday, December 12, 2012, 10:00 am - 11:45 am (final exam slot) in the usual class meeting room***

Brief Syllabus (for both semesters):

• Autumn Semester: we will learn how to treat fields (not particles!), such as electric and magnetic fields from the E&M class, as quantum-mechnical objects (how to "quantize" them). We will study the most important language of quantum field theory (and arguably of all of modern physics) - the language of Feynman diagrams. We will use Feynman rules to calculate cross sections for some (lowest order in the coupling constant) scattering processes. Formal topics are:
• Classical field theory
• Lorentz and Poincare groups and classification of fields
• Canonical quantization of free scalar, Dirac and electromagnetic fields
• Correlators in free field theory, Feynman propagator
• Interacting fields and Feynman diagrams
• Cross sections, S-matrix, and the LSZ reduction formula
• Quantum Electrodynamics (QED): cross section calculations for tree-level processes
• Spring Semester: we will find out that the Feynman diagrams at the higher (loop) orders in the coupling often lead to bad infinities. We will learn how to regulate the infinities (make them finite) and how to do them away altogether using the process or renormalization. We will then learn how to quantize the fields using Feynman's functional integrals, which is a beatiful alternative to canonical quantization. After that we will cover non-Abelian gauge theories, which are the backbone of the Standard Model of Particle Physics, as they explain both the strong and the electroweak interactions. We will study the theory of strong interactions - quantum chromodynamics (QCD). In the process we will have another scare as we will discover another sick infinity, the so-called Landau pole, and will learn why Landau did not believe in field theories. We will see why Landau's worries were wrong for QCD, but probably right for QED. We will then explore some special topics in Quantum Field Theory, several of which are listed below. Topics will be:
  • Radiative corrections, dimensional and Pauli-Villars regularizations, Ward identity
  • Renormalization group, renormalization of QED and scalar theories, running coupling constant
  • Functional integration
  • Non-Abelian gauge theories, Faddeev-Popov ghosts
  • Quantum Chromodynamics (QCD): asymptotic freedom and Landau pole, e^+e^- annihilation, Deep Inelastic Scattering (DIS) and parton model
  • Some special topics on demand: possibly quantum anomalies, instantons and other topological objects in field theory, DGLAP evolution, small-x physics and parton saturation, Electroweak theory, Higgs mechanism - the choice is up to you

Textbook:

• M. E. Peskin, D. V. Schroeder - An Introduction To Quantum Field Theory, Google Books

Recommended Reading :

• L. H. Ryder - Quantum Field Theory, Google Books
• C. Itzykson and J.-B. Zuber - Quantum Field Theory, Google Books
• P. Ramond - Field theory: a modern primer, Google Books
• M.A. Srednicki - Quantum Field Theory, Google Books
• S. Weinberg - The Quantum Theory of Fields, Google Books volume 1, volume 2, volume 3
• G. Sterman - An Introduction to Quantum Field Theory, Google Books

• H. Georgi - Lie Algebras in Particle Physics, Google Books

Lecture Notes:

• Classical Field Theory
  • Lecture 1
  • Lecture 2
  • Lecture 3 (part 1)
• Lorentz and Poincare Groups and Classification of Fields
  • Lecture 3 (part2)
  • Lecture 4
  • Lecture 5
  • Lecture 6
  • A more coherent presentation of spin in the Lorentz group
  • Lecture 7
  • Lecture 8
  • Lecture 9
• Canonical Quantization
  • Lecture 10
  • Lecture 11
  • Lecture 12
  • Lecture 13
  • Lecture 14
  • Lecture 15
  • Lecture 16 (part 1)
• Correlators in Free Field Theory
  • Lecture 16 (part 2)
  • Lecture 17
  • Lecture 18 (part 1)
• Interacting Fields and Feynman Diagrams
  • Lecture 18 (part 2)
  • Lecture 19
  • Lecture 20
  • Lecture 21
  • Lecture 22
  • Lecture 23
  • Lecture 24 (part 1)
• Cross Sections, S-Matrix, and the Reduction Formula
  • Lecture 24 (part 2)
  • Lecture 25
  • Lecture 26
  • Lecture 27
• Quantum Electrodynamics (QED): Tree-Level Processes
  • Lecture 28
  • Lecture 29
  • Lecture 30
  • Lecture 31
  • Lecture 32
  • Lecture 33 (part 1)

Homework Assignments:

Homeworks are due at 5 pm on the due date. Please put them in either my or the grader's mailboxes in PRB or give them to me in class or give them to the grader in his office, which is directly across from mine (or slide them under my office door if other options are not available).
(Solutions are password protected, they are for the use of OSU students and faculty only: if you are an OSU student or a faculty member and are interested in accessing them please write to me.)

• HW 1 (due Thursday, September 6) -- Solution 1
• HW 2 (due Tuesday, September 18) -- Solution 2
• HW 3 (due Thursday, October 4 --> deadline changed to Monday, October 8) -- Solution 3
• HW 4 (due Thursday, October 18) -- Solution 4
• HW 5 (due Thursday, November 1 --> deadline changed to Tuesday, November 6 ) -- Solution 5
• HW 6 (due Tuesday, November 20) -- Solution 6
• HW 7 (due Monday, December 10 --> deadline changed to Tuesday, December 11) -- Solution 7

Grading will be based on the HW's.