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

Advanced Mathematical Methods in Physics 1
PHYS-267 [CRN: 11015]: MWF, 3:30 - 4:20, TKH #103
[Topics ][ Daily Schedule ][ e-Gear ][Welcome ]

Instructor: Tristan Hübsch

TKH 213, 806-6267 thubsch@mac.com
Office hrs.: MW 11-12 & 4:30-5:30, and by appointment (at least one day ahead, confirmed)

Required Textbook and sources:

J. Wess & J. Bagger, Supersymmetry and Supergravity (2nd, rev. & exp. ed.)

 ◊1  T. Hubsch: Haploid (2,2)-Superfields in 2-Dimensional Spacetime

Nucl. Phys. B555(1999)567-628, hep-th/9901038.

 ◊2  R. Almukahhal & T. Hubsch: Haploid (2,2)-Superfields in 2-Dimensional Spacetime

Int. J. Mod. Phys. A16(2001)4713-4768, hep-th/9910007.

Recommended reading:

P. West, Supersymmetry and Supergravity
I.L. Buchbinder & S.M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity
M.T. Grisaru, M. Rocek, S.J. Gates, Jr., w. Siegel: 1001 Lessons in Supersymmetry

and other sources, as given in class

Component	Time	Remark	% of Grade
Term paper	Presented on 04/23/03	Topical	100%

The aim of the course is to introduce, develop and discuss various methods of supersymmetry and supergravity. Throughout the course, the emphasis is on the applications of these results rather than their proofs. The course is to be regarded as an statistically significant sampler rather than a definitive compendium, and students are strongly encouraged to study particular topics mentioned in the course, in detail and depth surpassing the discussions in class; this is the purpose of the term paper.

“Success = 1% inspiration + 99% perspiration”--T.A. Edison
But, learning is still 100% learnig + 0% teaching.

• The Supersymmetry Algebra, and its Basic Representations: §1-6
• Gauge Symmetry and Symmetry Breaking: §7-8
• Quantum Supersymmetry and Nonlinear Realizations: §9-11
• Differential Calculus in Superspace: §12-15
• Supergauge and Supergravity Models: §16-26
• (1,1|2,2)-Supersymmetry and Supergauge Symmetry: ◊1 & 2
• Other Dimensions: Sources Provided in Class
  

Day-to-day schedule: Students are expected to read ahead

01/17: Introductory Matters
01/20: Observed Holiday: Martin Luther King, Jr.'s Birthday
01/22: Why supersymmetry?: §1
01/24: The supersymmetry algebra and its representations:§2
01/27: Component fields:§3
01/29: Superfields:§4
01/31: Chiral (complex) superfields:§5
02/03: Vector (real) superfields:§6
02/05: Gauge invariance:§7
02/07: Spontaneous symmetry breaking:§8
02/10: Superfield propagators:§9
02/12: Feynman supergraphs:§10
02/14: Nonlinear realizations of supersymmetry:§11
02/17: Observed Holiday: Presidents' Day
02/19: Differential forms in superspace:§12
02/21: Gauge theories as constraint theories:§13
02/24: Vielbeins, torsion and curvature:§14
02/26: Binachi identities:§15
02/28: Supergauge transformations:§16
03/03: Lowest component fields of curvature tensors:§17
03/05: The supergravity multiplet:§18
03/07: Constrained superfields in curved space:§19
03/10: Chiral densities:§20
03/12: The minimal chiral supergravity:§21
03/14: Chiral models and Kähler geometry:§22
03/15-23: Spring Recess
03/24: General chiral supergravity models:§23
03/26: Gauge invariant models:§24
03/28: Gauge invariant supergravity models:§25
03/31: Low-energy theorems:§26
04/02: Peculiarities of (1,1|2,2)-superpsace:◊1
04/04: 1st order supercontraints - minimal haploid representations:◊1
04/07: Higher order superconstraints - nonminimal representations:◊1
04/09: Auxiliary and physical component fields:◊1
04/11: Gauge-covariant supersymmetry algebra:◊2
04/14: Inequivalent gauging of Yang-Mills type symmetries:◊2
04/16: An (in)complete classification:◊2
04/18: Other dimensions - group theory aspects: extra
04/21: Other dimensions - limitations in dimensions: extra
04/23: Student presentations

Collaboration policy

Collaboration -- but not blind copying -- on the homework assignments is strongly encouraged; students should use this to learn from each other. However, no collaboration is permitted on the term papers: by signing them, the students implicitly agree to abide by this policy. Violation of this policy is covered under University regulations on academic dishonesty and cheating.

Presentation and organization

While a neat presentation of home,- quiz- and exam-work 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 symbols such as the measure of an integral, arrow on a vector, vertical bars for the absolute value of a quantity, for the magnitude of a vector or for the determinant of a matrix, etc.

• Term paper: All students are required to write a term paper on a subject from the topical schedule and submit it by the last day of classes. A list of tentative topics will be presented in class, by the end of the first month of the course. The term papers must be typed or typeset in a format of a research paper, complete with references and any appropriate auxiliary material (tables, diagrams, figures, etc.), and are expected to be of a 15-page length

ADA disclaimer

Howard University is committed to providing an educational environment that is accessible to all students.  In accordance with this policy [details], students in need of accommodations due to a disability should contact the Office of the Dean for Special Student Services at 202-238-2420, for verification and determination of reasonable accommodations as soon as possible after admission to the Law School, or at the beginning of each semester.

© Tristan Hübsch, 2002