Annali di Matematica Pura ed Applicata

, Volume 130, Issue 1, pp 177–195 | Cite as

A symplectic framework of linear field theories

  • Wlodzimierz M. Tulczyjew


A framework for linear field theories based on the geometry of Lagrangian subspaces of symplectic spaces is formulated. Fields defined on finite compact domains and infinitesimal limits are treated in terms of de Rham currents. Field sources are included in the formulation. No distinction between elliptic and hyperbolic field equations is made.


Field Theory Field Equation Field Source Compact Domain Symplectic Space 
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    J. Dieudonné,Treatise on Analysis, Academic Press, New York and London (1972).Google Scholar
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    G. de Rham,Variétés différentiables, Hermann, Paris (1973).Google Scholar
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    W.M. Tulczyjew,The Legendre transformation, Ann. Inst. Henri Poincaré,27 (1977), pp. 101–114.Google Scholar
  4. [4]
    A.Weinstein,Lectures on symplectic manifolds, Regional Conference Series in Mathematics,29, A.M.S. (1976).Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1982

Authors and Affiliations

  • Wlodzimierz M. Tulczyjew
    • 1
  1. 1.Torino

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