Wigner-Type Theorems for Hilbert Grassmannians [E-Book] / Mark Pankov.
Pankov, Mark, (author)
Cambridge : Cambridge University Press, 2020
1 online resource (vii, 145 pages)
London Mathematical Society Lecture Note Series ; 460
Full Text
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.