Geometric Approach to Classical Phases

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


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:
$$ \Phi _g^* \Omega = \Omega . $$


Symplectic Manifold Geometric Approach Classical Phasis Horizontal Lift Reduce Phase Space 
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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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