Summary
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.
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References
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A.Weinstein,Lectures on symplectic manifolds, Regional Conference Series in Mathematics,29, A.M.S. (1976).
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Tulczyjew, W.M. A symplectic framework of linear field theories. Annali di Matematica pura ed applicata 130, 177–195 (1982). https://doi.org/10.1007/BF01761494
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DOI: https://doi.org/10.1007/BF01761494