Wigner-Type Theorems for Hilbert Grassmannians
Seiten
2020
Cambridge University Press (Verlag)
978-1-108-79091-8 (ISBN)
Cambridge University Press (Verlag)
978-1-108-79091-8 (ISBN)
Wigner's theorem plays an important role in the mathematical foundations of quantum mechanics. This book provides a quick, accessible introduction to the geometric approach to Wigner-type theorems, unifying both classical and more recent results, and is suitable for graduate students as well as more experienced researchers.
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.
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.
Mark Pankov is Professor of Mathematics at Uniwersytet Warmińsko-Mazurski, Poland. His research interests include preserver problems in operator theory related to quantum mechanics, geometry of linear codes, and zig-zags in discrete objects. He is the author of Grassmannians of Classical Buildings (2010) and Geometry of Semilinear Embeddings: Relations to Graphs and Codes (2015).
Introduction; 1. Two lattices; 2. Geometric transformations of Grassmannians; 3. Lattices of closed subspaces; 4. Wigner's theorem and its generalizations; 5. Compatibility relation; 6. Applications; References; Index.
| Erscheinungsdatum | 30.01.2020 |
|---|---|
| Reihe/Serie | London Mathematical Society Lecture Note Series |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 153 x 228 mm |
| Gewicht | 240 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 1-108-79091-7 / 1108790917 |
| ISBN-13 | 978-1-108-79091-8 / 9781108790918 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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