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Legendre Transformation for Regularizable Lagrangians in Field Theory

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Abstract

Hamilton equations based not only upon the Poincaré–Cartan equivalent of a first-order Lagrangian, but also upon its Lepagean equivalent are investigated. Lagrangians which are singular within the Hamilton–De Donder theory, but regularizable in this generalized sense are studied. Legendre transformation for regularizable Lagrangians is proposed and Hamilton equations, equivalent with the Euler–Lagrange equations, are found. It is shown that all Lagrangians affine or quadratic in the first derivatives of the field variables are regularizable. The Dirac field and the electromagnetic field are discussed in detail.

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  1. Mathematical Institute of the, Silesian University in Opava, Bezručovo nám. 13, 746 01, Opava, Czech Republic

    Olga Krupková & Dana Smetanová

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  1. Olga Krupková
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  2. Dana Smetanová
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Krupková, O., Smetanová, D. Legendre Transformation for Regularizable Lagrangians in Field Theory. Letters in Mathematical Physics 58, 189–204 (2001). https://doi.org/10.1023/A:1014548309187

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