 Covariant classical field theory

In recent years, there has been renewed interest in covariant classical field theory. Here, classical fields are represented by sections of fiber bundles and their dynamics is phrased in the context of a finitedimensional 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. Nonautonomous mechanics is formulated as covariant classical field theory on fiber bundles over the time axis .
Derivation and proof
The worksheet provides some of the geometric structure to the covariant formalism of firstorder classical field theories. Talk:Covariant classical field theory/workpage
See also
 Classical field theory
 Exterior algebra
 Variational bicomplex
 Quantum field theory
References
 Saunders, D.J., "The Geometry of Jet Bundles", Cambridge University Press, 1989, ISBN 0521369487
 Bocharov, A.V. [et al.] "Symmetries and conservation laws for differential equations of mathematical physics", Amer. Math. Soc., Providence, RI, 1999, ISBN 082180958X
 De Leon, M., Rodrigues, P.R., "Generalized Classical Mechanics and Field Theory", Elsevier Science Publishing, 1985, ISBN 0444877533
 Griffiths, P.A., "Exterior Differential Systems and the Calculus of Variations", Boston: Birkhauser, 1983, ISBN 3764331038
 Gotay, M.J., Isenberg, J., Marsden, J.E., Montgomery R., Momentum Maps and Classical Fields Part I: Covariant Field Theory, November 2003
 EcheverriaEnriquez, A., MunozLecanda, M.C., RomanRoy,M., Geometry of Lagrangian Firstorder Classical Field Theories, May 1995
 Giachetta, G., Mangiarotti, L., Sardanashvily, G., "Advanced Classical Field Theory", World Scientific, 2009, ISBN 9789812838957 (arXiv: 0811.0331v2)
Categories: Differential topology
 Differential equations
 Fiber bundles
 Theoretical physics
 Lagrangian mechanics
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