2023/12/08 by Jonathan Kelly, Kelly, Jonathan · 2 citations
Mathematics · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2312.07555
openalex publication_date 2023/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Galilean group of transformations that preserve spatial distances and absolute time intervals between events in spacetime. The special Galilean group, SGal(3), is a 10-dimensional Lie group; we examine the structure of the group and its Lie algebra and discuss the representation of uncertainty on the group manifold. Along the way, we mention several other groups, including the special orthogonal group, the special Euclidean group, and the group of extended poses, all of which are proper subgroups of the Galilean group. We describe the role of time in Galilean relativity and touch on the relationship between temporal and spatial uncertainty.