Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - I: The Standard Theory

TL;DR

This paper reformulates Newtonian gravity as a gauge theory based on the extended Galilei group, deriving the action principle through a limiting process from general relativity's ADM-DeWitt action.

Contribution

It introduces a gauge-theoretic formulation of Newtonian gravity using the extended Galilei group, connecting it to relativistic gravity via a limiting procedure.

Findings

Reformulation of Newtonian gravity as a gauge theory.

Derivation of the action principle from relativistic gravity.

Establishment of a connection between Newtonian and relativistic frameworks.

Abstract

Newton's standard theory of gravitation is reformulated as a {\it gauge} theory of the {\it extended} Galilei Group. The Action principle is obtained by matching the {\it gauge} technique and a suitable limiting procedure from the ADM-De Witt action of general relativity coupled to a relativistic mass-point.