Quantum Field Theory I
Physics 880.08, Fall 2009
Office: M2042 Physics Research Bldg
Office Hours: Tuesday 2:00 - 3:00 pm, Thursday 10:00 - 11:00 am
Course Meets: Mondays Wednesdays 12:30 pm - 2:18 pm, Scott Lab, room E0245.
Grader: Anastasios Taliotis
*** First Class Meets September 23, 2009 ***
*** There will be no classes on Wednesday, October 7, and on Monday, Wednesday, October 19, 21, 2009 - I'll be out of town.
***There will be a makeup class on Friday, October 16, 12:30 - 2:18 pm, Smith Lab, room 1042.
*** There will be another makeup class on Wednesday, November 11 (Veteran's Day), 10:30 am - 12:18 pm, we will meet at 10:30 am in PRB atrium and proceed to find a room for the class (either Smith seminar room or Smith Lab, room 1042).
*** There will be a makeup class on Monday, December 7, 11:30 am - 1:18 pm, at our usual location (this is the time slot for the final exam).
Brief Syllabus (for the three quarters):
- Fall quarter: 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). You'll see that this is not your mother's quantum mechanics! We will study the most important language of quantum field theory - the language of Feynman diagrams, and use it to calculate cross sections for some (lowest order in the coupling constant) scattering processes. Formal topics are:
- Canonical quantization of free scalar, Dirac and electromagnetic fields
- Feynman diagrams
- Cross section calculations for Quantum Electrodynamics (QED)
- Winter quarter: we will find out that much of what we have learned in the Fall quarter was lies, as Feynman diagrams at the higher (loop) orders in the coupling often lead to sick infinities. We will learn how to regulate the infinities (make them finite) and how to do them away altogether using the process or renormalization, thus saving the day. Topics will be:
- Functional integration, Ward identity
- Radiative corrections, dimensional and Pauli-Villars regularizations
- Renormalization group, running coupling constant
- Spring quarter: we will learn how to quantize 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 are:
- 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 - the choice is up to you guys
Recommended Reading :
Here's a list of books to complement Peskin and Schroeder. The books are listed in the order of
increasing difficulty (more or less).
- Classical Field Theory
- Lorentz and Poincare Groups and Classification of Fields
- Canonical Quantization
- Correlators in Free Field Theory
- Interacting Fields and Feynman Diagrams
Homeworks are due at 5 pm on the due date. Please put them in my or grader's mailboxes in PRB or give them to me in class (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 Wednesday, October 14) -- Solution 1 (problem numbering is a bit off in this solution, but you can recognize the problems by the solutions anyway)
- HW 2
(due Monday, November 2 --> deadline changed to Wednesday, November 4) -- Solution 2 (the same about problem numbers)
- HW 3 (due Wednesday, November 18) -- Solution 3
- HW 4 (due Friday, December 4 --> deadline changed to Wednesday, December 9) -- Solution 4
Grading will be based on the HW's.