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Geometry of Quantum Evolution

  • Dariusz Chruściński
  • Andrzej Jamiołkowski
Part of the Progress in Mathematical Physics book series (PMP, volume 36)

Abstract

Usually one uses completely different mathematical descriptions to formulate classical and quantum mechanics. Classical theory may be nicely formulated in terms of symplectic geometry, and the quantum one in terms of algebraic objects related to a complex Hilbert space. However, it turns out that standard, nonrelativistic quantum mechanics possesses natural geometric structure that is even richer than that found in classical mechanics. This section reveals the beauty of the geometric approach to quantum theory and stands as a basis for the elegant geometrical ideas of Pancharatnam and, later on, of Aharonov and Anandan.

Keywords

Mixed State Pure State Geometric Phase Qubit State Hermitian Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Dariusz Chruściński
    • 1
  • Andrzej Jamiołkowski
    • 1
  1. 1.Nicholas Copernicus UniversityTorunPoland

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