Divergences in formal variational calculus and boundary terms in Hamiltonian formalism

 Access to full text

 Full (PDF)

1. [Ald] S. J. Aldersley, Higher Eulerian operators and some of their applications, J. Math. Phys. 20 (1979), 522-531. Zbl0416.58028
2. [And76] I. M. Anderson, Mathematical foundations of the Einstein field equations, Ph. D. thesis, Univ. of Arizona, 1976. 
3. [And78] I. M. Anderson, Tensorial Euler-Lagrange expressions and conservation laws, Aequationes Math. 17 (1978), 255-291. Zbl0418.49041
4. [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. 
5. [Arn] V. I. Arnol'd, Mathematical methods of classical mechanics, Nauka, Moscow, 1974 (in Russian). 
6. [ADM] R. Arnowitt, S. Deser and C. W. Misner, Consistency of the canonical reduction of General Relativity, J. Math. Phys. 1 (1960), 434-439. Zbl0098.19103
7. [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. 
8. [Dorf] I. Dorfman, Dirac Structures and Integrability of Nonlinear Evolution Equations, John Wiley and Sons, New York, 1993. 
9. [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). 
10. [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. Zbl0716.58038
11. [KT] J. Kijowski and W. M. Tulczyjew, A symplectic framework for field theories, Lecture Notes in Phys. 107, Springer, New York, 1979. 
12. [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. Zbl0283.35022
13. [LMMR] D. Lewis, J. Marsden, R. Montgomery and T. Ratiu, The Hamiltonian structure for dynamic free boundary problems, Phys. D 18 (1986), 391-404. Zbl0638.58044
14. [LR] A. N. Leznov, A. V. Razumov, The canonical symmetry for integrable systems, J. Math. Phys. 35 (1994), 1738-1754. Zbl0801.58039
15. [Nij] A. Nijenhuis, Jacobi-type identities for bilinear differential concomitants of certain tensor fields. I, Indag. Math. 17 (1955), 390-397. Zbl0068.15001
16. [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. 
17. [Olv86] P. J. Olver, Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, Springer-Verlag, New York, 1986. 
18. [RT] T. Regge and C. Teitelboim, Role of surface integrals in Hamiltonian formalism of General Relativity, Ann. Physics 88 (1974), 286-318. Zbl0328.70016
19. [Sol85] V. O. Soloviev, Algebra of asymptotic Poincaré group generators in General Relativity, Teoret. Mat. Fiz. 65 (1985), 400-415 (in Russian). 
20. [Sol92] V. O. Soloviev, How canonical are Ashtekar's variables?, Phys. Lett. B 292 (1992), 30-34. 
21. [Sol93] V. O. Soloviev, Boundary values as Hamiltonian variables. I. New Poisson brackets, J. Math. Phys. 34 (1993), 5747-5769. Zbl0785.70014
22. [Sol94] V. O. Soloviev, Boundary values as Hamiltonian variables. II. Graded structures, q-alg/9501017, Preprint IHEP 94-145, Protvino, 1994.