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Communications in Mathematical Physics

, Volume 66, Issue 3, pp 197–221 | Cite as

Graded manifold theory as the geometry of supersymmetry

  • John Dell
  • Lee Smolin
Article

Abstract

Building upon Kostant's graded manifold theory, we present a new way of introducing spinors into the spacetime manifold, by expanding the algebra of functions on spacetime to a graded algebra. The elements of differential geometry are generalized to accomodate the expanded algebra of functions and in this enriched geometry we find the elements of supersymmetry and of supergravity theory. The geometrical role of the supergravity fields is discussed and a derivation of their transformation rules is given.

Keywords

Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • John Dell
    • 1
  • Lee Smolin
    • 2
  1. 1.Department of Physics and AstronomyUniversity of MarylandCollege ParkUSA
  2. 2.Lyman Laboratory of PhysicsHarvard UniversityCambridgeUSA

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