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.
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Geroch, R. (2004). Gauge, Diffeomorphisms, Initial-Value Formulation, Etc.. In: Chruściel, P.T., Friedrich, H. (eds) The Einstein Equations and the Large Scale Behavior of Gravitational Fields. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7953-8_13
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DOI: https://doi.org/10.1007/978-3-0348-7953-8_13
Publisher Name: Birkhäuser, Basel
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