Wigner-Type Theorems for Hilbert Grassmannians

Erscheinungsjahr 2020
ISBN: 978-1-108-79091-8
Verlag: Cambridge University Press

Buch, Englisch, Band 460, 152 Seiten, Format (B × H): 147 mm x 227 mm, Gewicht: 244 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Pankov, Mark

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

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.

Über Autor(innen)

Pankov, Mark
Mark Pankov is Professor of Mathematics at Uniwersytet Warminsko-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).