Covariant classical field theory

In mathematical physics, covariant classical field theory represents classical fields by sections of fiber bundles, and their dynamics is phrased in the context of a finite-dimensional space of fields. Nowadays, it is well known that[citation needed] jet bundles and the variational bicomplex are the correct domain for such a description. The Hamiltonian variant of covariant classical field theory is the covariant Hamiltonian field theory where momenta correspond to derivatives of field variables with respect to all world coordinates. Non-autonomous mechanics is formulated as covariant classical field theory on fiber bundles over the time axis ℝ.

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ReferencesEdit

  • Saunders, D.J., "The Geometry of Jet Bundles", Cambridge University Press, 1989, ISBN 0-521-36948-7
  • Bocharov, A.V. [et al.] "Symmetries and conservation laws for differential equations of mathematical physics", Amer. Math. Soc., Providence, RI, 1999, ISBN 0-8218-0958-X
  • De Leon, M., Rodrigues, P.R., "Generalized Classical Mechanics and Field Theory", Elsevier Science Publishing, 1985, ISBN 0-444-87753-3
  • Griffiths, P.A., "Exterior Differential Systems and the Calculus of Variations", Boston: Birkhäuser, 1983, ISBN 3-7643-3103-8
  • Gotay, M.J., Isenberg, J., Marsden, J.E., Montgomery R., Momentum Maps and Classical Fields Part I: Covariant Field Theory, November 2003 arXiv:physics/9801019
  • Echeverria-Enriquez, A., Munoz-Lecanda, M.C., Roman-Roy,M., Geometry of Lagrangian First-order Classical Field Theories, May 1995 arXiv:dg-ga/9505004
  • Giachetta, G., Mangiarotti, L., Sardanashvily, G., "Advanced Classical Field Theory", World Scientific, 2009, ISBN 978-981-283-895-7 (arXiv:0811.0331)