Abstract
In the preceding paper we developed a reformulation of Newtonian gravitation as a gauge theory of the extended Galilei group. In the present one we derive two generalizations of Newton's theory (a 10-fields and an 11-fields theory) in terms of an explicit Lagrangian realization of the absolute time dynamics of a Riemannian 3-space. They turn out to be gauge-invariant theories of the extended Galilei group in the same sense in which general relativity is said to be a gauge theory of the Poincaré group. The 10-fields theory provides a dynamical realization of some of the so-called `Newtonian spacetime structures' which have been classified geometrically by Künzle and Kuchar. The 11-fields theory involves a dilaton-like scalar potential in addition to a generalized Newtonian potential and, like general relativity, has a 3-metric with two dynamical degrees of freedom. It is interesting to find that, within the linear approximation, such degrees of freedom show graviton-like features: they satisfy a wave equation and propagate with a velocity related to the generalized scalar Newtonian potential.
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