The theory of symmetry actions in quantum mechanics: with an application to the Galilei group

Gianni Cassinelli, Ernesto De Vito, Pekka J. Lahti, Alberto Levrero (auth.)3540228020, 9783540228028

This is a book about representing symmetry in quantum mechanics. The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor. The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. The main concept of a symmetry action is defined as a group homomorphism from a given group, the group of symmetries, to the automorphism group of quantum mechanics. The structure of symmetry actions is determined under the assumption that the symmetry group is a Lie group. The Galilei invariance is used to illustrate the general theory by giving a systematic presentation of a Galilei invariant elementary particle. A brief description of the Galilei invariant wave equations is also given.

Table of contents :
1 A Synopsis of Quantum Mechanics….Pages 1-6
2 The Automorphism Group of Quantum Mechanics….Pages 7-25
3 The Symmetry Actions and Their Representations….Pages 27-47
4 The Galilei Groups….Pages 49-59
5 Galilei Invariant Elementary Particles….Pages 61-72
6 Galilei Invariant Wave Equations….Pages 73-87
A Appendix….Pages 89-101