"Wigner's theorem (67) provides a geometric characterization of unitary and anti-unitary operators as transformations of the set of rays of a complex Hilbert space, or equivalently, rank one projections. This statement plays an important role in mathematical foundations of quantum mechanic...

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Bibliographic Details

Main Author:	Pankov, Mark ca. 20./21. Jh (Author)
Format:	Book
Language:	English
Published:	Cambridge ; New York, NY ; Port Melbourne ; New Delhi ; Singapore Cambridge University Press 2020
Series:	London Mathematical Society lecture note series 460
Subjects:	Hilbert-Raum Graßmann-Mannigfaltigkeit Quantenmechanik Hilbert space Grassmann manifolds Geometry, Projective Quantum theory / Mathematics
Summary:	"Wigner's theorem (67) provides a geometric characterization of unitary and anti-unitary operators as transformations of the set of rays of a complex Hilbert space, or equivalently, rank one projections. This statement plays an important role in mathematical foundations of quantum mechanics (11; 50; 63), since rays (rank one projections) can be identified with pure states of quantum mechanical systems. We present various types of extensions of Wigner's theorem onto Hilbert Grassmannians and their applications. Most of these results were obtained after 2000, but to completeness of the exposition we include some classical theorems closely connected to the main topic (for example, Kakutani-Mackey's result on the lattice of closed subspaces of a complex Banach space (31), Kadison's theorem on transformations preserving the convex structure of the set of states of quantum mechanical systems (30)). We use geometric methods related to the Fundamental Theorem of Projective Geometry and results in spirit of Chow's theorem (13)"--
Item Description:	2002
Physical Description:	vii, 145 Seiten
ISBN:	9781108790918 1108790917