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Symplectic and Lagrangian Realization of Poisson Manifolds

In: Quantization, Coherent States, and Complex Structures

Author

Listed:
  • M. Giordano

    (Università Federico II, Dipartimento di Scienze Fisiche)

  • G. Marmo

    (Università Federico II, Dipartimento di Scienze Fisiche
    I.N.F.N.)

  • A. Simoni

    (Università Federico II, Dipartimento di Scienze Fisiche
    I.N.F.N.)

Abstract

An action principle is usually the starting point to describe physical systems, both particles and fields. A preliminary study usually considers fields as given, i.e. as external fields while particles are thought of as test particles, therefore only the point particle dynamics is dealt with. In this approach the Lagrangian function usually is the sum of three terms: a kinematic term which is quadratic in the velocities, a current-potential coupling term which is linear in the velocities, and a term which depends only on the positions, for instance the electrostatic potential.

Suggested Citation

  • M. Giordano & G. Marmo & A. Simoni, 1995. "Symplectic and Lagrangian Realization of Poisson Manifolds," Springer Books, in: J.-P. Antoine & S. Twareque Ali & W. Lisiecki & I. M. Mladenov & A. Odzijewicz (ed.), Quantization, Coherent States, and Complex Structures, pages 159-171, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-1060-8_18
    DOI: 10.1007/978-1-4899-1060-8_18
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