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

• DOI: 10.1007/s11040-006-9011-2
• Publication Date: 2006-12-01T13:12:28Z
• Authors: D. J. Hurley; M. A. Vandyck
• Keywords: Manifold (fluid mechanics); Linear map

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.