Classical field theories from Hamiltonian constraint: Canonical equations of motion and local Hamilton–Jacobi theory
2016 ◽
Vol 13
(06)
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pp. 1650072
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Keyword(s):
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton–Jacobi equation applicable in the field theory then follows readily. The general method is illustrated with three examples: non-relativistic Hamiltonian mechanics, De Donder–Weyl scalar field theory, and string theory.
2022 ◽
Vol 9
(2)
◽
pp. 136-141
2012 ◽
Vol 468
(2141)
◽
pp. 1391-1407
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Keyword(s):
Keyword(s):
1996 ◽
Vol 77
(20)
◽
pp. 4109-4113
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