DEPARTMENT OF PHYSICS AND ASTRONOMY -- (202) 806-6245 (main office), -5830 (fax)

Theoretical Physics 1 (216-238-01) MW 3⁰⁰-4³⁰ pm;
Office hrs.: MW 3 - 5, and by appointment (at least one day ahead, confirmed)
[Topics][Daily Schedule][Minimal Requirements][Assignments][e-Gear][Welcome]

Instructor: Tristan Hübsch

TKH#213, 806-6267 thubsch@mac.com

Textbook (required): M.E. Peskin, D.V. Schroeder: An Introduction to Quantum Field Theory

(opt.): F. Gross: Relativistic Quantum Mechanics and Field Theory
(opt.): S. Weinberg: The Quantum Theory of Fields, vol. I & II
(opt.): R.J. Rivers: Path Integral Methods in Quantum Field Theory
--- and several other sources, as given in class

Component	Due time	Remark	% of Grade
Homework	See in daily schedule	Late HW = 0 credit !!!	3 x 20%
Term project and presentation	End of class	25 min. + 10 min. questions	40%

The aim of the course is to give a brief but uncompromising introduction to Quantum Field Theory, some of the basic computational methods and techniques and to serve as a preparatory course for the second part (216-239-01), studying constrained models and supersymmetry. We begin with reviewing the necessity of passing from a quantum particle to quantum fields. The study of free spin-0 and -1/2 quantum fields will establish the basic formalism and introduce the perturbative approach to interactive field theory. This leads to a detailed study of renormalization, and a cursory inspection of so-called anomalies.

A successful student is expected to demonstrate a very good understanding of the fundamental principles of quantum field theory, but also to demonstrate-and maintain-the ability to solve practical problems involving quantum fields. For minimal requirements, see below!

Topical schedule:

We will cover the following material: (*** = fully, ** = partially, * = skim)

Part I:Feyman Diagrams and Quantum Electrodynamics

§1: Invitation: Pair Production of e⁺e^- Annihilation - ***
§2: The Klein-Gordon Field - ***
§3: The Dirac Field - ***
§4: Interacting Fields and Feynman Diagrams - ***
§5: Elementary Processes in Quantum Electrodynamics - **
§6: Radiative Corrections: Introduction - *
§7: Radiative Corrections: Some Formal Developments - **

Part II: Renormalization

§8: Invitation: Ultraviolet Cutoffs and Critical Fluctuations - ***
§9: Functional Methods - ***
§10: Systematics of Renormalization - **
§11: Renormalization and Symmetry - ***
§12: The Renormalization Group - **

Part III: Non-Abelian Gauge Theories - *

§19: Perturbation Theory Anomalies - *

Day-to-day schedule: Students are required to read ahead and discuss in class!

Last year's schedule; will be modified soon.

08/24: Introductory matters
08/26: The need for fields, §1
08/28: From classical to quantum (scalar) fields, §2.1-2.3
08/31: Quantum (scalar) fields in spacetime, §2.4
09/02: The Dirac equation, §3.1-3.4
09/07: Observed Holiday: Labor Day
09/09: Quantum Dirac spinors, §3.5-3.6
09/14: Covariant perturbation theory & Feyman diagrams, §4.1-4.3
09/16: Feynman diagrams & the S-matrix, §4.4-4.5 [HW#1 due]
09/21: S-matrix elements from Feynman diagrams, §4.6-4.8
09/23: e⁺e^- --> µ⁺µ^-, and e⁺e^- --> (hadrons) processes §5.1-5.3
09/28: Mandelstam variables, the Klein-Nishina formula, §5.4-5.5
09/30: Bremsstrahlung, the electron vertex & IR divergences, §6.1-6.5
10/05: The field-strength & charge renormalization, optical theorem & Ward-Takashi identity, §7.1-7.5
10/07: UV divergences and cutoffs, §8
10/12: Observed Holiday: Columbus Day
10/14: Functional quantization of scalar fields, Quantum field theory vs. statistical mechanics §9.1-9.3
10/19: Quantization of the spin-1/2 and spin-1 fields & symmetries §9.4-9.6 [HW#2 due]
10/21: Counting (grading) of UV divergences, §10.1
10/26: Renormalized perturbation theory, §10.2-10.5
10/28: Spontaneous symmetry breaking §11.1
11/02: Renormalization and symmetry, §11.2
11/04: The effective action, §11.3-11.5
11/09: Renormalization and symmetry (again), §11.6
11/11: Wilson's renormalization theory, Callan-Symanzik equation §12.1-12.2
11/16: The evolution of coupling (non)-constants, §12.3 [HW#3 due]
11/18: Renormalization of local operators, evolution of mass parameters §12.4-12.5
11/23: The axial current in two and four spacetime dimensions, §19.1-19.2
11/25: Goldstone bosons, chiral symmetries & anomalies, anomalous scale-non-invariance §19.3-19.5
11/30: presentations
12/02: presentations

Minimum requirements:

To pass the course with a grade B or better, a graduate Student must at the time of the presentation of the term project be able to demonstrate the ability to:

1. read off the Feynman “diagrammatics” from a Lagrangian density;
2. complete the calculation of a one-loop (contribution to a) process;
3. discuss the qualitative behavior of the renormalization flow in simple models;
4. clearly explain the physics content, technical setting and method of analysis and calculations and their physics interpretations of the presentation topic.

A graduate student who cannot demonstrate the above listed skills at the time of the presentation of the term project automatically forfeits a grade of B or better -- regardless of the total number of points acquired in homework, and regardless of the success in completing any other course requirement.

Homework assignments

1. Due 09/16: 2.1, 2.2, 3.1, 3.8
2. Due 10/19: 4.1, 4.2, 5.3, 7.2
3. Due 11/16: 9.1, 9.2, 10.2, 11.2

All homework assignments are due by 5:00 pm of the day indicated and should be either given to the instructor in hand, left in the instructor's mailbox in TKH#105, or slid under the instructor's office door, TKH#213. Late homework will not be accepted, except in cases of proven (medical) emergency.

Collaboration policy
Collaboration -- but not blind copying -- on the homework and term paper assignments is strongly encouraged; students should use this to learn from each other. However, each student must demonstrate a good understanding of the presentation topic - at the presentation. Failure to do so would imply covered under University regulations on academic dishonesty and cheating.

Coursework presentation and organization
While a neat presentation of homework is not required for full credit, it certainly makes it easier to assess the quality of the work and give the proper credit due. In all cases, include a simple sketch if it might help conveying the approach or the calculations. Where necessary, include: all units and complete symbols, such as the precise measure and limits of an integral, etc., and references for all quoted and cited material.

• Homework: Submitted answer sheets should be stapled (preferably in the top-left corner). The Student's full name (and ID number) should be indicated on the first (cover) page. Solutions should be labeled and ordered consecutively by the problem numbers. Include all calculation/work and give full reference to any result quoted from any source other than the text, and page/equation number for results quoted from the text or otherwise.
• Term paper and presentation: Each student will freely choose a topic for the term project from among the chapters in the required text. The project will then consist of exploring the references given in the text, performing sample calculations and writing a 15-20 page review paper. This review will also be presented in a 20-25 minute talk, with a 10-15 minute question period at the end. The students are expected to start on the project at least one month before the end of the due date, and interact with the instructor and among each other as much as possible. The paper and the presentation are expected to be at the professional level.

© Tristan Hübsch, 2000