Tensor fields defining a tangent bundle structure
de Filippo, Sergio ; Landi, Giovanni ; Marmo, Giuseppe ; Vilasi, Gaetano
Annales de l'I.H.P. Physique théorique, Tome 51 (1989), p. 205-218 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPA_1989__50_2_205_0,
     author = {de Filippo, Sergio and Landi, Giovanni and Marmo, Giuseppe and Vilasi, Gaetano},
     title = {Tensor fields defining a tangent bundle structure},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {51},
     year = {1989},
     pages = {205-218},
     mrnumber = {1002820},
     zbl = {0752.58010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1989__50_2_205_0}
}

de Filippo, Sergio; Landi, Giovanni; Marmo, Giuseppe; Vilasi, Gaetano. Tensor fields defining a tangent bundle structure. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) pp. 205-218. http://gdmltest.u-ga.fr/item/AIHPA_1989__50_2_205_0/

[1] C. Itzykson and J.B. Zuber, Quantum Field Theory, McGraw-Hill. N. Y. 1980. L.D. Faddeev and A.A. Slavnov, Gauge Fields. Introduction to Quantum Theory, Benjamin/Cummings, London, 1980. | MR 585517

B.S. De Witt, Quantum Theory of Gravity I: The Canonical Theory. Phys. Rev., t. 160, 1967, p. 1113. | Zbl 0158.46504

B.S. De Witt, Quantum Theory of Gravity II; The manifestely Covariant Theory. Phys. Rev., t. 162, 1967, p. 1195-1239. | Zbl 0161.46501

B.S. De Witt, Quantum Theory of Gravity III ; Applications of Covariant Theory. Phys. Rev., t. 162, 1967, p. 1239-1256. | Zbl 0161.46501

[2] P.A.M. Dirac, Lectures on Quantum Mechanics. Belfer Graduate School of Science Monographs Series n. 2, N.Y. 1964.

E.C.G. Sudarshan and N. Mukunda, Classical Dynamics: A Modern Perspective. Wiley and Sons, N. Y. 1974. | MR 434047 | Zbl 0329.70001

A. Hanson, T. Regge and C. Teitelboim, Constrained Hamiltonian Systems. Accademia Nazionale dei Lincei Roma 1976.

[3] L.D. Faddeev, Feynman Integral for Singular Lagrangian. Theor. Math. Phys., t. 1, 1970, p. 1. | MR 465005

[4] R. Abraham and J. Marsden, Foundations of Mechanics. Benjamin Reading, Massachussets, 1978. | MR 515141 | Zbl 0393.70001

[5] G. Marmo, E.J. Saletan, A. Simoni and B. Vitale, Symmetry and Reduction of Dynamical Systems. Wiley and Sons, N. Y. 1985. | MR 818988

P. Libermann and C.M. Marle, Symplectic Geometry and analitical Mechanics. | MR 851386 | Zbl 0643.53002

D. Reidel Dordrecht, 1987.

K. Yano and S. Ishimara, Tangent and Cotangent Bundles. Marcel Dekker, 1973. | MR 350650 | Zbl 0262.53024

M. Crampin, Tangent Bundle Geometry for Lagrangian Dynamics. J. Phys., t. A16, 1983, p. 3755-3772. | MR 727054 | Zbl 0536.58004

[6] G. Marmo, N. Mukunda and J. Samuel, Dynamics and Symmetry for Constrained Systems; A Geometrical Analysis. La Rivista del Nuovo Cimento, t. 6, 1983, p. 2. | MR 729476

J. Gotay, J. Nester and G. Hinds, Presymplectic Manifolds and the Dirac-Bergman Theory of Constraints. J. Math. Phys., t. 19, 1978, p. 2388. | MR 506712 | Zbl 0418.58010

J. Gotay and J. Nester, Presymplectic Lagrangian Systems I: The Constraint Algorithm and the Equivalence Theorem. Ann. Inst. H. Poincaré, t. 30A, 1979, p. 129-142. | Numdam | MR 535369 | Zbl 0414.58015

J. Gotay and J. Nester, The Second Order Equation Problem. Ann. Inst. H. Poincaré, t. 32A, 1980, p. 1-13. | Numdam | MR 574809 | Zbl 0453.58016

[7] G. Morandi, C. Ferrario, G. Lo Vecchio, G. Marmo and C. Rubano, The Inverse Problem in the Calculus of Variations and the Geometry of the Tangent Bundle. Naples Preprint, 1987. | MR 1050526 | Zbl 1211.58008

H.P. Kunzle, Canonical Dynamics of Spinning Particles in Gravitational and Electromagnetic Fields. J. Math. Phys., t. 13, 1972, p. 739-744. | MR 299139 | Zbl 0232.70018

F. Cantijn, J.F. Carinena, M. Crampin and L.A. Ibort, Reduction of degenerate Lagrangian Systems. J. Geom. Phys., t. 3, 1986, p. 3. | MR 894631 | Zbl 0621.58020

[8] A.P. Balachandran, G. Marmo, B.S. Skagerstam and A. Stern, Gauge Symmetries and Fibre Bundles. Lecture Notes in Physics, 1988, p. 188. | MR 717218 | Zbl 0525.53065

[9] P. Tondeur, Introduction to Lie Groups and Transformation Group. Lecture Notes in Math., n° 7 Springer Verlag, 1969. | Zbl 0198.05001

[10] T. Nagano, 1-Forms With the Exterior derivative of Maximal Rank. J. Differential Geometry, t. 2, 1968, p. 253-264. | MR 239526 | Zbl 0172.46903

[11] J. Klein, Structures symplectiques ou J-symplectiques homogènes sur l'espace tangent à une variété. Sympos. Math., t. 14, 1974, p. 181-192. | MR 388449 | Zbl 0306.53037

J. Klein, Proc. IUTAM-ISIMM symposium on modern developments in analytical mechanics. S. Benenti, M. Francaviglia and A. Lichnerowicz eds. Pitagora (Bologna 1984).

[12] M. Crampin, Defining Euler-Lagrange Fields in Terms of Almost Tangent Structures. Phys. Lett., t. 95A, 1983, p. 466-468. | MR 708702

[13] M. Crampin and G. Thompson, Affine Bundles and Integrable Almost Tangent Structures. Math. Proc. Camb. Phil. Soc., t. 98, 1985, p. 61-71. | MR 789719 | Zbl 0572.53031