Mathematical Aspects of Superspace

Over the past five years, through a continually increasing wave of activity in the physics community, supergravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the spectrum of elementary particles. C...

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Corporate Author: SpringerLink (Online service)
Other Authors: Seifert, H.J. (Editor), Clarke, C.J.S. (Editor), Rosenblum, A. (Editor)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1984, 1984
Edition:1st ed. 1984
Series:Nato Science Series C:, Mathematical and Physical Sciences
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Non-linear Realization of Supersymmetry
  • 1. Introduction
  • 2. The Akulov-Volkov field
  • 3. Superfields
  • 4. Standard fields
  • 5. N > 1/N = 1
  • 6. N = 1 supergravity
  • References
  • Fields, Fibre Bundles and Gauge Groups
  • 1. Manifolds
  • 2. Fibre bundles
  • 3. Gauge Groups
  • 4. Space-Time
  • Path Integration on Manifolds
  • 1. Introduction
  • 2. Gaussian measures, cylinder set measures, and the Feynman-Kac formula
  • 3. Feynman path integrals
  • 4. Path integration on Riemannian manifolds
  • 5. Gauge invariant equations; diffusion and differential forms
  • Acknowledgements, References
  • Graded Manifolds and Supermanifolds
  • Preface and cautionary note
  • 0. Standard notation
  • 1. The category GM
  • 2. The geometric approach
  • 3. Comparisons
  • 4. Lie supergroups
  • Table: “All I know about supermanifolds”
  • References
  • Aspects of the Geometrical Approach to Supermanifolds
  • 1. Abstract
  • 2. Building superspace over an arbitrary spacetime
  • 3. Super Lie groups
  • 4. Compact supermanifolds with non-Abelian fundamental group
  • 5. Developments and applications
  • References
  • Integration on Supermanifolds
  • 1. Introduction
  • 2. Standard integration theory
  • 3. Integration over odd variables
  • 4. Superforms
  • 5. Integration on Er,s
  • 6. Integration on supermanifolds
  • References
  • Remarks on Batchelor’s Theorem
  • Classical Supergravity
  • 1. Definition of classical supergravity
  • 2. Dynamical analysis of classical field theories
  • 3. Formal dynamical analysis of classical supergravity
  • 4. The exterior algebra formulation of classical supergravity
  • 5. Does classical supergravity make sense?
  • Appendix: Notations and conventions
  • References
  • List of participants