Gauge, Diffeomorphisms, Initial-Value Formulation, Etc.

  • Robert Geroch
Conference paper

Abstract

We introduce a large class of systems of partial differential equations on a base manifold M, a class that, arguably, includes most systems of physical interest. We then give general definitions — applicable to any system of equations in this class — of “having the diffeomorphisms on M as a gauge group”, and, for such a system, of “having an initial-value formulation, up to this gauge”. These definitions, being algebraic in the coefficients of the partial differential equations, are relatively easy to check in practice. The Einstein system, of course, satisfies our definitions.

Keywords

Partial Differential Equation Vector Field Gauge Transformation Gauge Condition Derivative Operator 
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 Basel AG 2004

Authors and Affiliations

  • Robert Geroch
    • 1
  1. 1.Enrico Fermi InstituteChicagoUSA

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