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0741.70012
Gotay,
Mark J.
A multisymplectic framework for classical field theory and the calculus
of variations. I: Covariant Hamiltonian formalism. (English)
[CA] Mechanics, analysis and geometry: 200 years after Lagrange, 203-235
(1991).
The present paper is the first in a series devoted to a new approach to
classical field theory and the calculus of variation. It develops a covariant
Hamiltonian formalism in the calculus of variations which will provide a
general and systematic means of canonically analyzing any Lagrangian variational
principle. The key ingredients in this work are: (i) a new candidate for
the covariant phase space, which carries a canonically defined multisymplectic
structure; (ii) the construction of the corresponding Legendre transformation
from a given Lepagean equivalent of the Lagrangian density; and (iii) a
suitable definition of regularity in the higher order case. These results
comprise the foundation of a truly Hamiltonian framework for the calculus
of variations in general, and enable one to deal directly with higher order
Lagrangians as well as multiple integrals.
[ B.Cheshankov
(Sofia) ]
Keywords: classical field theory; calculus of variation; covariant
Hamiltonian formalism; Lagrangian variational principle; multisymplectic
structure; Legendre transformation
Citations:
Zbl
0714.00021