nLab Galilean group

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Contents

Contents

Idea

The Euclidean group Iso(D)Iso(D) is the isometry group of Euclidean space D\mathbb{R}^D, generated from rigid translations rotations and reflections.

For D=3D=3 this is part of the canonical symmetry group of ordinary nonrelativistic classical mechanics/classical field theory, thus known as the Galilean group, which in addition contains time-translations and “Galilean boosts”:

This is a 10 dimensional Lie group which may be understood as the Inönü-Wigner contraction of the Poincaré group given by the limit in whuch the speed of light goes to infinity.

References

Textbook account:

See also:

Last revised on August 4, 2025 at 08:39:05. See the history of this page for a list of all contributions to it.