Theory of super LIE groups
The theory of supergravity has attracted increasing attention in the recent years as a unified theory of elementary particle interactions. The superspace formulation of the theory is highly suggestive of an underlying geometrical structure of superspace. It also incorporates the beautifully geometrical general theory of relativity. It leads us to believe that a better understanding of its geometry would result in a better understanding of the theory itself, and furthermore, that the geometry of superspace would also have physical consequences. As a first step towards that goal, we develop here a theory of super Lie groups. These are groups that have the same relation to a super Lie algebra as Lie groups have to a Lie algebra. More precisely, a super Lie group is a super-manifold and a group such that the group operations are super-analytic. The super Lie algebra of a super Lie group is related to the local properties of the group near the identity. This work develops the algebraic and super-analytical tools necessary for our theory, including proofs of a set of existence and uniqueness theorems for a class of super-differential equations.
- Research Organization:
- Brandeis Univ., Waltham, MA (USA)
- OSTI ID:
- 5794277
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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645400* - High Energy Physics- Field Theory