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Wigner-Type Theorems for Hilbert Grassmannians
About This Book
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.
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Table of contents
- Cover
- Series page
- Title page
- Copyright page
- Contents
- Preface
- Introduction
- 1 Two Lattices
- 2 Geometric Transformations of Grassmannians
- 3 Lattices of Closed Subspaces
- 4 Wignerâs Theorem and Its Generalizations
- 5 Compatibility Relation
- 6 Applications
- References
- Index