| 释义 |
- See also
- References
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{{cn|date=February 2016}} 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., [https://arxiv.org/pdf/physics/9801019 Momentum Maps and Classical Fields Part I: Covariant Field Theory], November 2003
- Echeverria-Enriquez, A., Munoz-Lecanda, M.C., Roman-Roy,M., [https://arxiv.org/abs/dg-ga/9505004 Geometry of Lagrangian First-order Classical Field Theories], May 1995
- Giachetta, G., Mangiarotti, L., Sardanashvily, G., "Advanced Classical Field Theory", World Scientific, 2009, {{ISBN|978-981-283-895-7}} (arXiv: 0811.0331v2)
5 : Differential topology|Differential equations|Fiber bundles|Theoretical physics|Lagrangian mechanics |