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1997 | 39 | 1 | 373-388
Tytuł artykułu

Divergences in formal variational calculus and boundary terms in Hamiltonian formalism

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
Słowa kluczowe
Rocznik
Tom
39
Numer
1
Strony
373-388
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Institute for High Energy Physics 142 284, Protvino, Moscow region, Russia
Bibliografia
  • [Ald] S. J. Aldersley, Higher Eulerian operators and some of their applications, J. Math. Phys. 20 (1979), 522-531.
  • [And76] I. M. Anderson, Mathematical foundations of the Einstein field equations, Ph. D. thesis, Univ. of Arizona, 1976.
  • [And78] I. M. Anderson, Tensorial Euler-Lagrange expressions and conservation laws, Aequationes Math. 17 (1978), 255-291.
  • [And92] I. M. Anderson, Introduction to the variational bicomplex, in: Mathematical aspects of classical field theory, M. J. Gotay, J. E. Marsden and V. Moncrief (eds.), Contemp. Math. 132, AMS, Providence, 1992.
  • [Arn] V. I. Arnol'd, Mathematical methods of classical mechanics, Nauka, Moscow, 1974 (in Russian).
  • [ADM] R. Arnowitt, S. Deser and C. W. Misner, Consistency of the canonical reduction of General Relativity, J. Math. Phys. 1 (1960), 434-439.
  • [BH] J.D. Brown and M. Henneaux, On the Poisson brackets of differential generators in classical field theory, J. Math. Phys. 27 (1986), 489-491.
  • [Dorf] I. Dorfman, Dirac Structures and Integrability of Nonlinear Evolution Equations, John Wiley and Sons, New York, 1993.
  • [GD] I. M. Gel'fand and L. A. Dickey, Asymptotics of Sturm-Liouville equation resolvent and algebra of Korteweg-de Vries equation, Uspekhi Mat. Nauk 30 (1975), 67-100 (in Russian).
  • [JK] J. Jezierski and J. Kijowski, The localization of energy in gauge field theories and in linear gravitation, Gen. Relativity Gravitation 22 (1990), 1283-1307.
  • [KT] J. Kijowski and W. M. Tulczyjew, A symplectic framework for field theories, Lecture Notes in Phys. 107, Springer, New York, 1979.
  • [KMGZ] M. D. Kruskal, R. M. Miura, C. S. Gardner and N. J. Zabusky, Korteweg-de Vries equation and generalizations. V. Uniqueness and nonexistence of polynomial conservation laws, J. Math. Phys. 11 (1970), 952-960.
  • [LMMR] D. Lewis, J. Marsden, R. Montgomery and T. Ratiu, The Hamiltonian structure for dynamic free boundary problems, Phys. D 18 (1986), 391-404.
  • [LR] A. N. Leznov, A. V. Razumov, The canonical symmetry for integrable systems, J. Math. Phys. 35 (1994), 1738-1754.
  • [Nij] A. Nijenhuis, Jacobi-type identities for bilinear differential concomitants of certain tensor fields. I, Indag. Math. 17 (1955), 390-397.
  • [Olv84] P. J. Olver, Hamiltonian perturbation theory and water waves, in: Fluids and Plasmas: Geometry and Dynamics, J. E. Marsden (ed.), Contemp. Math. 28, AMS, Providence, 1984.
  • [Olv86] P. J. Olver, Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, Springer-Verlag, New York, 1986.
  • [RT] T. Regge and C. Teitelboim, Role of surface integrals in Hamiltonian formalism of General Relativity, Ann. Physics 88 (1974), 286-318.
  • [Sol85] V. O. Soloviev, Algebra of asymptotic Poincaré group generators in General Relativity, Teoret. Mat. Fiz. 65 (1985), 400-415 (in Russian).
  • [Sol92] V. O. Soloviev, How canonical are Ashtekar's variables?, Phys. Lett. B 292 (1992), 30-34.
  • [Sol93] V. O. Soloviev, Boundary values as Hamiltonian variables. I. New Poisson brackets, J. Math. Phys. 34 (1993), 5747-5769.
  • [Sol94] V. O. Soloviev, Boundary values as Hamiltonian variables. II. Graded structures, q-alg/9501017, Preprint IHEP 94-145, Protvino, 1994.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv39z1p373bwm
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