Wigner-Type Theorems for Hilbert Grassmannians

Description

Wigner's theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics. At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results. Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications. An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers. Cover......Page 1 LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES......Page 2 Wigner-Type Theorems for Hilbert Grassmannians ......Page 4 Copyright ......Page 5 Contents ......Page 6 Preface......Page 8 Introduction......Page 10 1 Two Lattices......Page 13 2 Geometric Transformations of Grassmannians......Page 31 3 Lattices of Closed Subspaces......Page 62 4 Wigner’s Theorem and Its Generalizations......Page 77 5 Compatibility Relation......Page 111 6 Applications......Page 134 References......Page 150 Index......Page 154