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Geometric Approach to Classical Phases

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

Abstract

Suppose that (\( {\cal P} \) , Ω) is a symplectic manifold and let G be a Lie group acting from the left on \( {\cal P} \) by canonical transformations. That is, there is a mapping
$$ \Phi :G \times {\cal P} \to {\cal P}, $$
such that for any gG,
$$ \Phi _g :{\cal P} \to {\cal P}, $$
defined by Φ g = Φ(g, ·), is a canonical transformation:
$$ \Phi _g^* \Omega = \Omega . $$

Keywords

Symplectic Manifold Geometric Approach Classical Phasis Horizontal Lift Reduce Phase Space 
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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