The Problem of Invariance for Covariant hamiltonians

 Access to full text

 Full (PDF)

1. [1] M. F. ATIYAH, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc., 85 (1957), pp. 181-207. Zbl0078.16002MR86359
2. [2] D. BLEECKER, Gauge Theory and Variational Principles, Addison-Wesley Publishing Company, Inc., Reading, MA, 1981. Zbl0481.58002MR643361
3. [3] M. CASTRILLÓN LÓPEZ - J. MUÑ OZ MASQUÉ, The geometry of the bundle of connections, Math. Z., 236 (2001), pp. 797-811. Zbl0977.53020MR1827505
4. [4] M. CRAMPIN - E. MARTÍNEZ - W. SARLET, Linear connections for systems of second-order ordinary differential equations, Ann. Inst. H. Poincaré Phys. Théor., 65, no. 2 (1996), pp. 223-249. Zbl0912.58002MR1411267
5. [5] D. J. ECK, Gauge-natural bundles and generalized gauge theories, Mem. Amer. Math. Soc., 247 (1981). Zbl0493.53052MR632164
6. [6] ANTONIO FERNÁNDEZ - PEDRO L. GARCÍA - J. MUÑOZ MASQUÉ, Gaugeinvariant covariant Hamiltonians, J. Math. Phys., 41 (2000), pp. 5292-5303. Zbl0993.37028MR1770956
7. [7] PEDRO L. GARCÍA, Gauge algebras, curvature and symplectic structure, J. Differential Geom., 12 (1977), pp. 209-227. Zbl0404.53033MR650115
8. [8] PEDRO L. GARCÍA - J. MUÑ OZ MASQUÉ, Differential invariants on the bundles of linear frames, J. Geom. Phys., 7, (1990), pp. 395-418. Zbl0764.53017MR1120933
9. [9] H. GOLDSCHMIDT - S. STERNBERG, The Hamilton-Cartan formalism in the calculus of variations, Ann. Inst. Fourier (Grenoble), 23, no. 1 (1973), pp. 203-267. Zbl0243.49011MR341531
10. [10] V. GUILLEMIN - S. STERNBERG, Symplectic techniques in physics, Cambridge University Press, Cambridge, UK, 1983. Zbl0576.58012MR770935
11. [11] S. KOBAYASHI - K. NOMIZU, Foundations of Differential Geometry, Volume I, John Wiley & Sons, Inc., N.Y., 1963. Zbl0119.37502MR152974
12. [12] J. L. KOSZUL, Fibre bundles and Differential Geometry, Tata Institute of Fundamental Research, Bombay, 1960. Zbl0244.53026
13. [13] L. MANGIAROTTI - G. SARDANASHVILY, Connections in classical and quantum field theory, World Scientific Publishing Co., Inc., River Edge, NJ, 2000. Zbl1053.53022MR1764255
14. [14] J. MARSDEN - S. SHKOLLER, Multisymplectic geometry, covariant Hamiltonians, and water waves, Math. Proc. Cambridge Phil. Soc., 125 (1999), pp. 553-575. Zbl0922.58029MR1656833
15. [15] E. MASSA - E. PAGANI, Jet bundle geometry, dynamical connections, and the inverse problem of Lagrangian mechanics, Ann. Inst. H. Poincaré Phys. Théor., 61, no. 1 (1994), pp. 17-62. Zbl0813.70004MR1303184
16. [16] J. MUÑOZ MASQUÉ, Formes de structure et transformations infinitésimales de contact d'ordre supérieur, C.R. Acad. Sci. Paris, 298, Série I (1984), pp. 185-188. Zbl0598.58002MR741091
17. [17] J. MUÑ OZ MASQUÉ, An axiomatic characterization of the Poincaré-Cartan form for second-order variational problems, Lecture Notes in Math. 1139, Springer-Verlag, 1985, pp. 74-84. Zbl0578.58011MR820469
18. [18] J. MUÑOZ MASQUÉ - M. E. ROSADO, Invariant variational problems on linear frame bundles, J. Phys. A: Math. Gen., 35 (2002), pp. 2013-2036. Zbl1029.70013MR1892125
19. [19] P. J. OLVER, Equivalence, Invariants, and Symmetry, Cambridge University Press, Cambridge, UK, 1995. Zbl0837.58001MR1337276
20. [20] G. A. SARDANASHVILY, Gauge Theory in Jet Manifolds, Hadronic Press Monographs in Applied Mathematics, Hadronic Press, Inc., Palm Harbor, FL, U.S.A., 1993. Zbl0811.58004MR1262598
21. [21] D. J. SAUNDERS, The Geometry of Jet Bundles, Cambridge University Press, Cambridge, UK, 1989. Zbl0665.58002MR989588
22. [22] D. J. SAUNDERS - M. CRAMPIN, On the Legendre map in higher-order field theories, J. Phys. A: Math. Gen., 23 (1990), pp. 3169-3182. Zbl0761.58006MR1063014
23. [23] R. UTIYAMA, Invariant theoretical interpretation of interaction, Phys. Rev., 101 (1956), 1597-1607. Zbl0070.22102MR78223