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3 results

  • 1 - Two Lattices

  • Mark Pankov
  • Book:
    Wigner-Type Theorems for Hilbert Grassmannians
    Published online:
    06 January 2020
    Print publication:
    16 January 2020, pp 4-21

  • Summary

    This is a brief description of basic properties of the lattice formed by all subspaces of a vector space and the orthomodular lattice consisting of all closed subspaces of a complex Hilbert space. The first lattice is investigated in classical projective geometry, the second is related to the logical structure of quantum mechanical systems.

Wigner-Type Theorems for Hilbert Grassmannians
  • Mark Pankov
  • Published online:
    06 January 2020
    Print publication:
    16 January 2020
  • 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.