Abstract. Newton's standard theory of gravitation is reformulated in terms of a generally Galilei-covariant action principle as a gauge theory of the extended Galilei group. A suitable modification of Utiyama's method for gauging the projective realization of the Galilei group associated with the free mass-point, together with the connections between the consequent 11 external gauge fields and known facts about Galilean and Newtonian geometrical structures, are discussed from a unified point of view. Then the problem of the existence of an action principle for the dynamical evolution of the gauge fields is analysed. Since it is not known how to extend Utiyama's method from the case of `invariance' to the case of `quasi-invariance, modulo the equations of motion', which turns out to be the key factor in the Galilean case, an action principle is derived, starting from a suitable power expansion of the 4-metric tensor, as a contraction, for , of the ADM-De-Witt action of general relativity. The Galilean action depends on 27 fields (i.e. it contains 16 auxiliary fields besides the 11 gauge fields) and is indeed quasi-invariant, modulo the equations of motion under general Galilean coordinate transformations. The physical equivalence of this theory and Newton's theory of gravity is shown explicitly, by analysing its first- and second-class constraints. Finally, we discuss the feasibility of a symplectic reduction of the 27-fields theory to a minimal theory depending on only the 11 gauge fields, in the sense of Utiyama's method.

PACS numbers: 0450, 0490, 0350

Print publication: Issue 1 (January 1995)
Received 6 May 1994, in final form 30 August 1994