Wigner-Type Theorems for Hilbert Grassmannians

An accessible introduction to the geometric approach to Wigner's theorem and its role in quantum mechanics.

Mark Pankov (Author)

9781108790918, Cambridge University Press

Paperback / softback, published 16 January 2020

152 pages
22.8 x 15.3 x 1 cm, 0.24 kg

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.

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.

Subject Areas: Mathematical physics [PHU], Quantum physics [quantum mechanics & quantum field theory PHQ], Geometry [PBM], Functional analysis & transforms [PBKF]