Mathematical Physics, Analysis and Geometry

, Volume 9, Issue 3, pp 203–223 | Cite as

A Geometrical Interpretation of ‘Supergauge’ Transformations Using D-Differentiation

  • D. J. Hurley
  • M. A. Vandyck


D-transport is employed to construct, within the limited setting of a non-graded manifold, a geometrical framework that yields a generalisation of the ‘supergauge’ transformations of Supergravity. Killing’s equation is shown to be at the origin of the ‘gauged’ supersymmetry transformations. The presence of a field-dependent Lorentz transformation is traced to the fact that, for every given X, the difference of two D-differentiation operators \({^1\!D}_X\) and \({^2\!D}_X\) is a linear transformation that necessarily depends on X.

Key words

supergravity gauge transformation D-differentiation 

Mathematics Subject Classifications (2000)

83E50 58C20 58Z05 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of MathematicsNational University of IrelandCorkIreland
  2. 2.Department of PhysicsNational University of IrelandCorkIreland

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