n-symplectic algebra of observables in covariant Lagrangian field theory

Journal of Mathematical Physics

Volumn 42, Issue 10, 2001, Pages 4827-4845

  Norris, L K ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035537088     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1396835     Document Type: Article

References (30)

1. B. Kostant, in Lectures in Modern Analysis III, Lecture Notes in Mathematics, edited by C. T. Taam (Springer, Berlin, 1970). Vol. 170.
2. J.-M. Souriau. Structure des Systèmes Dynamiques (Dunod, Paris, 1970).
3. L. K. Norris. "Generalized symplectic geometry on the frame bundle of a manifold." Lecture given at the AMS Summer Research Institute on Differential Geometry, 1990, at the University of California at Los Angeles.
4. L. K. Norris, Generalized Symplectic Geometry on the Frame Bundle of a Manifold, Proc. Symp. Pure Math., Part 2 (American Mathemetical Society Providence, RI, 1993). Vol. 54, pp. 435-465.
5. L. K. Norri,. "Symplectic geometry on T* M derived from n-symplectic geometry on LM," J. Geom. Phys. 13, 51-78 (1994).
6. L. K. Norris, "Schouten-Nijenhuis Brackets," J. Math. Phys. 38, 2694-2709 (1997).
7. R. O. Fulp, J. K. Lawson, and L. K. Norris, "Geometric prequantization on the spin bundle based on n-symplectic geometry: The Dirac equation," Int. J. Theor. Phys. 33, 1011-1028 (1994).
8. R. O. Fulp, J. K. Lawson, and L. K. Norris, "Generalized symplectic geometry as a covering theory for the Hamiltonian theories of classical particles and fields," J. Geom. Phys. 20, 195-206 (1996).
9. M. MacLean and L. K. Norris, "Covariant field theory on frame bundles of fibered manifolds," J. Math. Phys. 41. 6808-6823 (2000).
10. L. K. Norris and M. Salgado, "n-symplectic geometric quantization of covariant Lagrangian field theories," (in preparation).
11. I. V. Kanatchikov, "Covariant geometric prequantization of fields." LANL archive gr-qc/0012038: "On the Duffin-Kemmer-Petiau formulation of the covariant Hamiltonian dynamics in field theory," Rep. Math. Phys. 46, 107-112 2000), LANL archive hep-th/9911175; "Precanonical quantization and the Schrödinger wave functional." Phys. Lett. A 283, 25-36 (2001), LANL archive hep-th/0012084.
12. I. V. Kanatchikov, "Covariant geometric prequantization of fields." LANL archive gr-qc/0012038: "On the Duffin-Kemmer-Petiau formulation of the covariant Hamiltonian dynamics in field theory," Rep. Math. Phys. 46, 107-112 (2000), LANL archive hep-th/9911175; "Precanonical quantization and the Schrödinger wave functional." Phys. Lett. A 283, 25-36 (2001), LANL archive hep-th/0012084.
13. C. Günther, "The polysymplectic Hamiltonian formalism in field theory and the calculus of variations." J. Diff. Geom. 25. 23-53 (1987).
14. S. P. Hrabak, "On a multisymplectic formulation of the classical BRST symmetry for first order field theories part II: Geometric structures," LANL archive math-ph/9901013: "On a multisymplectic formulation of the classical brst symmetry for first order field theories part I: Algebraic structures," LANL archive math-ph/9901012.
15. M. Gotay, J. Isenberg, J. Marsden R. Montgomery, J. Sniatycki, and P. Yasskin, "Momentum maps and classical relativistic fields" (MSRI preprint).
16. J. K. Lawson, "Generalized symplectic geometry for classical fields and spinors." Ph.D. dissertation. Department of Mathematics North Carolina State University Raleigh, North Carolina. 1994.
17. J. A. Scheuten, "Uber differentialkomitanten zweier kontravarianter grossen," Proc. K. Ned. Akad. Wet. 43, 449-452 (1940).
18. A. Nijenhuis. "Jacobi-type identities for bilinear differential concomitants of certain tensor fields." Indag. Math. 17, 390-403 (1955).
19. A. Awane, "k-symplectic structures." J. Math. Phys. 33, 4046-4052 (1992): "Structures k-symplectiques." Doctoral dissertation. Mulhouse. 1992.
20. M. de León. I, Mendez, and M. Salgado, "p-almost cotangent structures. Bolletino Unione Matematica Italiana." 7-a. 97-107 (1993): "Regular p-almost cotangent structures," J. Kor. Math. Soc. 25, 273-287 (1988): M. de León, E. Merino, J. Oubiña, P. Rodrigues, and M. Salgado. "Hamiltonian systems on k-cosymplectic manifolds." J. Math. Phys. 39, 876-893 (1997): M. de Leon, E. Merino, and M. Salgado. "A-cosympleclic manifolds and Lagrangian field theory" (preprint); M. de León, J. Oubiña, and M. Salgado. "Integrable almost s-tangent structures," Rendi. Mat. Ser. VII 14, 609-623 (1994).
21. M. de León. I, Mendez, and M. Salgado, "p-almost cotangent structures. Bolletino Unione Matematica Italiana." 7-a. 97-107 (1993): "Regular p-almost cotangent structures," J. Kor. Math. Soc. 25, 273-287 (1988): M. de León, E. Merino, J. Oubiña, P. Rodrigues, and M. Salgado. "Hamiltonian systems on k-cosymplectic manifolds." J. Math. Phys. 39, 876-893 (1997): M. de Leon, E. Merino, and M. Salgado. "A-cosympleclic manifolds and Lagrangian field theory" (preprint); M. de León, J. Oubiña, and M. Salgado. "Integrable almost s-tangent structures," Rendi. Mat. Ser. VII 14, 609-623 (1994).
22. M. de León. I, Mendez, and M. Salgado, "p-almost cotangent structures. Bolletino Unione Matematica Italiana." 7-a. 97-107 (1993): "Regular p-almost cotangent structures," J. Kor. Math. Soc. 25, 273-287 (1988): M. de León, E. Merino, J. Oubiña, P. Rodrigues, and M. Salgado. "Hamiltonian systems on k-cosymplectic manifolds." J. Math. Phys. 39, 876-893 (1997): M. de Leon, E. Merino, and M. Salgado. "A-cosympleclic manifolds and Lagrangian field theory" (preprint); M. de León, J. Oubiña, and M. Salgado. "Integrable almost s-tangent structures," Rendi. Mat. Ser. VII 14, 609-623 (1994).
23. M. de León. I, Mendez, and M. Salgado, "p-almost cotangent structures. Bolletino Unione Matematica Italiana." 7-a. 97-107 (1993): "Regular p-almost cotangent structures," J. Kor. Math. Soc. 25, 273-287 (1988): M. de León, E. Merino, J. Oubiña, P. Rodrigues, and M. Salgado. "Hamiltonian systems on k-cosymplectic manifolds." J. Math. Phys. 39, 876-893 (1997): M. de Leon, E. Merino, and M. Salgado. "A-cosympleclic manifolds and Lagrangian field theory" (preprint); M. de León, J. Oubiña, and M. Salgado. "Integrable almost s-tangent structures," Rendi. Mat. Ser. VII 14, 609-623 (1994).
24. M. de León. I, Mendez, and M. Salgado, "p-almost cotangent structures. Bolletino Unione Matematica Italiana." 7-a. 97-107 (1993): "Regular p-almost cotangent structures," J. Kor. Math. Soc. 25, 273-287 (1988): M. de León, E. Merino, J. Oubiña, P. Rodrigues, and M. Salgado. "Hamiltonian systems on k-cosymplectic manifolds." J. Math. Phys. 39, 876-893 (1997): M. de Leon, E. Merino, and M. Salgado. "A-cosympleclic manifolds and Lagrangian field theory" (preprint); M. de León, J. Oubiña, and M. Salgado. "Integrable almost s-tangent structures," Rendi. Mat. Ser. VII 14, 609-623 (1994).
25. N. Woodhouse, Geometric Quantization, 2nd ed. (Oxford University Press, Oxford, 1992).
26. T. de Donder, Théorie Invariantive du Calcul des Variations, Nouvelle Edit. (Gauthier-Villars, Paris, 1935); H. Weyl, "Geodesic fields in the calculus of variations for multiple integrals." Ann. Math. 36, 607-629 (1935).
27. T. de Donder, Théorie Invariantive du Calcul des Variations, Nouvelle Edit. (Gauthier-Villars, Paris, 1935); H. Weyl, "Geodesic fields in the calculus of variations for multiple integrals." Ann. Math. 36, 607-629 (1935).
28. H. Rund, The Hamilton-Jacobi Theory in the Calculus of Variations, Reprinted Edition (Krieger, Huntington, 1973).
29. C. Carathéodory, "Uber die Variationsrechnung bei mehrfachen integralen." Acta Szeged Sect. Scient. Math. 4, 193-216 (1929).
30. Daniel Cartin, M.S. thesis, "Some aspects of geometric prequantization on the affine frame bundle." North Carolina State University, Raleigh North Carolina, 1995.