Relativity, Symmetry and the Structure of the Quantum Theory

The history of how quantum mechanics was developed is a fascinating one and underlies the focus of this book; namely, given the rules that the founders of quantum mechanics developed, is it possible to find principles that lead to the structure of quantum mechanics as it was historically formulated? This is the first book in a series of works considering what particular relativity is applicable to a given dynamical theory. The series considers Newton, Einstein, and de Sitter relativities while this book examines the unitary irreducible representations of the Galilei group and see how they provide the framework for Galilean quantum theory. Quantum mechanics was developed in the early 20th century; arising from the desire to understand the behaviour of atoms and molecules, systems that surprisingly did not follow the known rules of classical mechanics. So new rules had to be created, rules that used classical mechanics as a starting point, but then deviated significantly from most of the principal concepts underlying classical mechanics. The answer given in this book is that principles incorporating relativity and symmetry are sufficient to ground quantum mechanics.