Group contraction in physics: History and potential

Abstract

This article serves as a review of the mathematical tool of group contraction with an emphasis on physical applications. It was implicitly understood that some theories contain others as a special case (e.g., the relation between special relativity and Newtonian mechanics), but until the 1950s there was no firm mathematical grounding for such relations. We discuss the historical development of these concepts, their application to symmetry groups of space and time, and their relevance to the phenomenon of spontaneous symmetry breaking. Finally, we close by proposing a speculative chronology of space-time symmetries in the early universe.