Wigner-Type Theorems for Hilbert Grassmannians

✍ Scribed by Mark Pankov

• Publisher: Cambridge University Press
• Year: 2020
• Tongue: English
• Leaves: 154
• Series: London Mathematical Society Lecture Note Series 460
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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