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Legendre transformation for regularizable Lagrangians in field theory. (English) Zbl 1005.70025
Summary: We investigate Hamilton equations based not only on Poincaré-Cartan equivalent of a first-order Lagrangian, but also on its Lepagean equivalent. We study Lagrangians which are singular within the Hamilton-De Donder theory, but regularizable in this generalized sense. Legendre transformation is proposed for regularizable Lagrangians, and Hamilton equations are found which are equivalent to Euler-Lagrange equations. It is shown that all Lagrangians, affine or quadratic in first derivatives of field variables, are regularizable. Finally, we discuss in detail Dirac field and electromagnetic field.

70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
58Z05 Applications of global analysis to the sciences
78A25 Electromagnetic theory (general)
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