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 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.
See also
Classical field theory
Exterior algebra
Lagrangian system
Variational bicomplex
Quantum field theory
Non-autonomous mechanics
Higgs field (classical)
References
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)
Hellenica World - Scientific Library
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