Supralgebras, supergroups and geometric gauging
(I) This highly mathematical part deals with superalgebras, supergroups, and supermanifolds under the following headings: supers enter physics and mathematics; superalgebras; superconformal and super-Poincare algebras; the Z(2) and Z graded Grassman rings: supermanifolds; the classification of simple Lie superalgebras; classical superalgebras: the superlinear (or superunitary) sequences; classical superalgebras: the orthosymplectic sequences; classical hyperexceptional and exceptional superalgebras; nonclassical superalgebras; and supergroups. (II) It appears plausible that some type of Supergravity might provide a unifying principle for Gravity and the other interactions. Gauging a supergroup has yielded an embedding of the Weinberg-Salam model of asthenodynamics in a highly constraining aesthetic theory. In this part, dealing with forms on a (rigid) group manifold, a principal bundle, and a soft (Dali) group manifold, the elements of the exterior calculus are developed on a Lie group manifold. Then the geometric theory of gauging is obtained; for a local internal symmetry, this is done on a principal bundle. For a noninternal group, such as the Poincare or super-Poincare group, Gravity and Supergravity are reproduced by use of a soft group manifold, i.e., a manifold the tangent of which is the original rigid group. The theory is expounded along according to the following program: differential geometry and Lie groups; examples: the Poincare and super-Poincare groups; gauge theory over a principal fiber bundle; ghosts and BRS equations; the soft group manifold; weakly reducible symmetric groups; geometric quadratic Lagrangian for WRSS groups; Gravity; and Supergravity.
- Research Organization:
- Texas Univ., Austin (USA). Center for Particle Theory
- DOE Contract Number:
- AS05-76ER03992
- OSTI ID:
- 5293217
- Report Number(s):
- ORO-3992-384; TRN: 80-011976
- Country of Publication:
- United States
- Language:
- English
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