INSTITUTE FOR ADVANCED STUDY
			  School of Mathematics
			  Princeton, NJ  08540





QUANTUM FIELD THEORY SEMINARS

SPEAKER:   Joseph Bernstein, Tel Aviv University

TIME:  2:00 P.M. TO 4:00 P.M.

LOCATION:  M-101

			TENTATIVE AGENDA


Tuesday, September 17, 1996

Lecture 1. What physicists have in mind when they talk about SUSY 
(supersymmetry).                

1. Bosons and fermions - Z_2 grading on the Hilbert space  of states.
2. General idea about groups of symmetries. Symmetries of 
Lagrangian and symmetries of Hilbert space.
   Groups of symmetries containing Poincare group P.
3. Coleman Mandula theorem. Possibility to discover supersymmetries.
4.Supergroups containing P. 
5.N-extended supersymmetry algebra.


Thursday, September 19, 1996

Lecture 2.  Basics of super mathematics.

1.Super linear algebra. ( Example: Lie superalgebras).
2. Definition of superscheme and supermanifold
3. Differential geometry on supermanifolds:
   Tangent bundle.              
   DeRham complex
4. Frobenius pairing and Frobenius theorem
5. Construction of supermanifolds. Families
   Example: V(F).
6. Variety M~. Two constructions. Connection with DeRham theory.
7. Supergroups and super Lie algebras. Lie theory.


Tuesday, September 24, 1996

Lecture 3. Integration theory and \sigma-models

I. Integration theory.

1. Definition of volume forms
2. Definition of integral
3. How to compute super integral?

II. \sigma-models

1. Usual 2-dimensional \sigma model
2. Supersymmetric 2-dimensional \sigma model
3. Reduction to classical integrals - component analisys and 
elimination of auxiliery fields.
4. Off-shell and on-shell SUSY


September 26, 1996

Thursday, Lecture 4. Wess-Zumino model on flat space ( d = 4, N = 1).

1. Construction of the flat SUSY space. Structures.
2. Chiral functions.
3. Chiral fields and Young-Mills Lagrangian.
4. General Lagrangian.
5. Reduction to the classical integral
6. Of shell and on-shell SUSY.
7. Generaliztion to \sigma model in Kahler manifolds
8. Dimensional reduction and extended N = 2 off shell theory for d = 2.


Tuesday, October 1, 1996

Lecture 5. Simple supergravity ( d = 4, N = 1).

1. Conformal structure
2. Connection between volume bundles
3. Supergravity
4. Partial connection. Decomposition into direct sum
5. Definition in terms of connection and constrains.


Thursday, October 3, 1996

Lecture 6. Higher dimensional theories.

1. Nahm's theorem
2. 10-dimensional Young-Mills.
3. Dimensional reduction - N = 4 Young-Mills theory in dimension 4
4. 11-dimensional supergravity. reduction to extended 
   (d=4,N=8)-gravity.

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