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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.

MSC:
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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