Geometry of Quantum Evolution

Part of the Progress in Mathematical Physics book series (PMP, volume 36)


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.


Mixed State Pure State Geometric Phase Qubit State Hermitian Manifold 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  1. 1.Nicholas Copernicus UniversityTorunPoland

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