A note on Legendre transformations. (English) Zbl 0782.58024
Summary: Constructions for Legendre transformations and Cartan forms in Lagrangian field theories are described for both first-order and higher-order systems. The uniqueness of the constructions for higher-order systems is discussed, with particular attention to the case of second-order systems.
MSC:
| 37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
| 70Sxx | Classical field theories |
References:
| [1] | Aldaya, V.; De Azcárraga, J. A., Higher-order Hamiltonian formalism in field theory, J. Phys. A: Math. Gen., 13, 2545-2551 (1980) · Zbl 0467.58013 |
| [2] | Cariñena, J. F.; Crampin, M.; Ibort, L. A., On the multisymplectic formalism for first-order field theories (1989), The Open University: The Open University Milton Keynes, Preprint · Zbl 0782.58057 |
| [3] | Crampin, M., Tangent bundle geometry for Lagrangian dynamics, J. Phys. A: Math. Gen., 16, 3755-3772 (1983) · Zbl 0536.58004 |
| [4] | M. Gotay, private communication.; M. Gotay, private communication. |
| [5] | Kuperschmidt, B. A., Geometry of jet bundles and the structure of Lagrangian and Hamiltonian formalism, (Geometric Methods in Mathematical Physics, 775 (1980), Springer: Springer Berlin), 162-218, Lecture Notes in Math. · Zbl 0439.58016 |
| [6] | Saunders, D. J., An alternative approach to the Cartan form in Lagrangian field theories, J. Phys. A: Math. Gen., 20, 339-349 (1987) · Zbl 0652.58002 |
| [7] | Saunders, D. J., The Geometry of Jet Bundles, (LMS Lecture Note Series, 142 (1989), Cambridge University Press) · Zbl 0665.58002 |
| [8] | D.J. Saunders and M. Crampin, On the Legendre map in higher-order field theories (in preparation).; D.J. Saunders and M. Crampin, On the Legendre map in higher-order field theories (in preparation). · Zbl 0761.58006 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
