Short CommunicationsNo Access

ON HIGHER DERIVATIVES AS CONSTRAINTS IN FIELD THEORY: A GEOMETRIC PERSPECTIVE

L. VITAGLIANO

L. VITAGLIANO

Dipartimento di Matematica, Università degli Studi di Salerno, Via Ponte don Melillo, 84084 Fisciano (SA), Italy

Instituto Nazionale di Fisica Nucleare, GC di Salerno - Sezione di Napoli, via Cintia, 80126 Naples, Italy

Levi-Civita Institute, via Colacurcio 54, 83050 Santo Stefano del Sole (AV), Italy

Search for more papers by this author

https://doi.org/10.1142/S0219887811005968Cited by:5 (Source: Crossref)

Abstract

We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.

Keywords:

AMSC: 53B50, 53C80, 70S05

References

A. M. Vinogradov, J. Math. Anal. Appl. 100, 1 (1984), DOI: 10.1016/0022-247X(84)90071-4. Crossref, Web of Science, Google Scholar
A. M. Vinogradov, J. Math. Anal. Appl. 100, 41 (1984), DOI: 10.1016/0022-247X(84)90072-6. Crossref, Web of Science, Google Scholar
N. Román-Roy, SIGMA 5, 100 (2009), arXiv: math-ph/0506022. Google Scholar
Th. de Donder, Théorie Invariantive du Calcul des Variations (Gauthier Villars, Paris, 1935) pp. 95–108. Google Scholar
L. Vitagliano, J. Geom. Phys. 60, 857 (2010), arXiv: 0905.4580 DOI: 10.1016/j.geomphys.2010.02.003. Crossref, Web of Science, Google Scholar
C. M. Camposet al., J. Phys. A: Math. Theor. 42, 775,207 (2009), arXiv: 0906.0389. Google Scholar
R. Skinner, J. Math. Phys. 24, 2581 (1983), DOI: 10.1063/1.525653. Crossref, Web of Science, Google Scholar
R. Skinner and R. Rusk, J. Math. Phys. 24, 2589 (1983), DOI: 10.1063/1.525654. Crossref, Web of Science, Google Scholar
R. Skinner and R. Rusk, J. Math. Phys. 24, 2595 (1983), DOI: 10.1063/1.525655. Crossref, Web of Science, Google Scholar
V. Aldaya and J. de Azcárraga, J. Phys. A: Math. Gen. 13, 2545 (1982), DOI: 10.1088/0305-4470/13/8/004. Crossref, Google Scholar
L. Vitagliano, Partial differential Hamiltonian systems, submitted for publication (2010) , arXiv: 0903.4528 . Google Scholar
P. L. García, A. García and C. Rodrigo, J. Geom. Phys. 56, 571 (2006). Crossref, Web of Science, Google Scholar
A. V. Bocharov et al. , Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, Translations of Mathematical Monographs 182 ( American Mathematical Society , Providence , 1999 ) . Google Scholar
I. S. Krasil'shchik , V. V. Lychagin and A. M. Vinogradov , Geometry of Jet Spaces and Nonlinear Differential Equations , Advanced Studies in Contemporary Mathematics 1 ( Gordon and Breach , New York, London , 1986 ) . Google Scholar
J. E. Marsdenet al., J. Geom. Phys. 38, 253 (2001), arXiv: math/0005034 DOI: 10.1016/S0393-0440(00)00066-8. Crossref, Web of Science, Google Scholar