Covariant classical field theory
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In recent years, there has been renewed interest in covariant classical field theory. Here, dynamics are phrased in the context of a finite-dimensional space of fields at a given event in spacetime. Nowadays, it is well known that jet bundles are the correct domain for such a description.
[edit] Derivation and proof
The worksheet provides some of the geometric structure to the covariant formalism of first-order classical field theories. Covariant classical field theory::worksheet
[edit] See also
[edit] 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 082180958X
- 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: Birkhauser, 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
- Echeverria-Enriquez, A., Munoz-Lecanda, M.C., Roman-Roy,M., Geometry of Lagrangian First-order Classical Field Theories, May 1995
