Delaware State University
Department of Applied Mathematics and Theoretical Physics
Dover, DE 19901
Introduction to Supersymmetry
60-721-00,
3 cr.
Text:
J. Wess & J. Bagger:
T. Hubsch:
Supersymmetry and Supergravity, 2nd ed.
research literature excerpts and class-notes
recommended:
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
P. West:
Supersymmetry and Supergravity
The aim of the course is to introduce, develop and discuss various methods relating to
supersymmetry, as invented originally in high-energy particle physics, and then developed as superfunctional analysis in superspace. The course offers a statistically significant introductory sampler of
topics rather than a definitive compendium of all areas. 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.
Prerequisite: Mathematical methods of Physics IV (26-667) or equivalent (vector calculus, linear
algebra, tensors, real and complex analysis, multivariate calculus). A successful student is expected to
gain a working knowledge of the covered material, so as to be able to (1) follow the applications in the
literature, (2) solve typical problems in the field, and (3) discuss adequately the term-paper subject.
Topical schedule:
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Lie Algebras, superalgebras and their representations
Lie bracket; Jacobi identities; Graded extension; Representations and modules
The Supersymmetry Algebra,
Poincaré algebra and its supersymmetric extension; on-shell representations
(extension of Wigner’s classification); off-shell linear representations
Supersymmetry in 1-dimensional time: Supersymmetric Quantum Mechanics
Supermultiplets and Adinkras; Adinkra topology; topography and classification
Supersymmetry in higher-dimensional spacetime: Supersymmetry and Superspace
Supermultiplets and superfunctions; Functional analysis in superspace
Supersymmetric Dynamics
Supermmetric Lagrangian densities & equations of motion; Super-currents and Noether’s
theorem; Boundary conditions and spontaneous supersymmetry breaking
Supersymmetric Gauge Interactions
Gauge-covariant superderivatives; Field strengths, non-physical fields and prepotentials
Supersymmetric Curved Field Space
Supersymmetric sigma-models; Zamolodchikov’s metric; Moduli spaces
Supersymmetric Curved Spacetime
Pure supergravity; Coupling to matter, Super Weyl anomaly & trace anomaly
1. Course Title/Number:
Introduction to Supersymmetry / 60-721-00
2. Number of Credits:
3
CURRICULUM COURSE REVIEW:
Introduction to Supersymmetry
3. Curriculum Program Title: Ph.D. in Applied Mathematics and Theoretical Physics
4. Curriculum/Course is:
[X]
New
[
[
Required Course
[X]
]
]
Revised
Elective Course
5. List Prerequisites:
26-667 (Mathematical methods of Physics IV), or equivalent (vector calculus, linear algebra,
tensors, real and complex analysis, multivariate calculus)
6. List Courses Being Replaced or Changed:
This is a new course.
7. List Courses Being Deleted:
No courses are being deleted.
8. Needs Statement:
This course is indispensable for students pursuing a Ph.D. in theoretical physics with interest in
fundamental physics, but may also serve well other students of theoretical physics. Supersymmetry is a
transformation of bosons into fermions and vice versa, which leaves certain hallmark qualities and
quantitative descriptors of a system unchanged—or, when spontaneously broken, predictably different.
Such phenomena occur throughout microscopic (molecular, atomic, nuclear and sub-nuclear) physics,
and provide the foundation for understanding the quantum stability of the real vacuum, the correlation in
the nuclear structure of isotopes and hypermuclei, etc.
9. Catalog Description of the Course:
The course introduces, develops and discusses various methods relating to supersymmetry and
supersymmetry breaking, as invented originally in high-energy particle physics, but also including
applications in various other branches of microscopic physics.
10. List of Objectives of the Course:
(1) To provide an introduction to the body knowledge and techniques of super-mathematics
(super-analysis, super-algebras and super-groups), as applied in theoretical physics. (2) To see how these
techniques apply to the analysis of phenomena in microscopic physics. (3) To learn how to identify
those phenomena throughout theoretical physics, which are best described using these methods. (4) To
develop the problem-solving skills associated with the application of these methods in theoretical
physics, and learn how to extract experimentally verifiable information from such application.
CURRICULUM COURSE REVIEW:
Superstrings and Beyond
11. Course Outline:
See the “Topical schedule” section in the attached brief syllabus.
12. Show how the proposed course fits into the curriculum or course sequence:
This course is an elective within the curriculum of the Ph.D. program in theoretical physics, and
is indispensable for students focusing on fundamental physics. For an overview of pre-requisite
dependences and the course’s relation to other courses proposed herein, please see the attached
“Proposed Course Dependencies” chart.
13. Are there comparable courses in other departments?
No.
14. How will the students be affected by this course change?
This course provides the students an opportunity to increase their integration with the research
program of the Department of Applied Mathematics and Theoretical Physics, by understanding the
mathematical underpinnings of the techniques that are used in contemporary theoretical physics. This
course will improve students’ professional competence, employability in technical fields and ability to
pass professional examinations; the term paper requirement will foster improving expository skills.
Neither this course nor its prerequisites increase the total number of semester hours in this curriculum or
the number of credit hours required for graduation.
15. What effect will this new course have on College resource?
None: this course will not require new or additional resources or staffing.
16. How will the course benefit the College?
This course will study the structure of supersymmetry, and its appearance and effects in
microscopic and fundamental physics. This emphasizes the symmetry structure of the contemporary,
unified understanding of physics and so may serve also as an elective to students pursuing a Ph.D.
degree in other scientific or philosophical fields.
17. How will the change affect the program?
This course will introduce students to the use of super-mathematics and its application in various
branches of physics. This course will be one of the electives specific to the Ph.D. program
(concentration in theoretical physics) in this department. Besides providing such a cross-disciplinary
CURRICULUM COURSE REVIEW:
Introduction to Supersymmetry
broadening of knowledge for the students in this program, it also serves as a prerequisite to Introduction
to superstrings, also proposed herein.
18. Evaluation of Student Performance:
Homework Assignments
40 %
Term-paper (take-home final)
60 %
Sample homework assignments, in-term and final examination question-sheets, work sheets,
course notes, review sheets and term papers will be accessible on-line.
Course Structure: Three (3) 50-minute lectures per week.
References
1. J. Wess & J. Bagger: Supersymmetry and Supergravity, 2nd ed. (Princeton University Press,
1992, ISBN = 0691025304)
2. I. L. Buchbinder & S. M. Kuzenko: Ideas and Methods of Supersymmetry and Supergravity
(Taylor & Francis, 1998; ISBN = 0750305061)
3. M. T. Grisaru, M. Rocek, S. J. Gates, Jr., W. Siegel: 1001 Lessons in Supersymmetry (AddisonWesley, 1983; ISBN = 0805331611)
4. P. West: Supersymmetry and Supergravity (World Scientific, 1990, ISBN = 9810200994)
Submitted to Department of Applied Mathematics and Theoretical Physics
by: Tristan Hubsch, on 27th of November, 2007.