Canonical Noether symmetries and commutativity properties for gauge systems

Journal of Mathematical Physics

Volumn 41, Issue 11, 2000, Pages 7333-7351

  Gràcia, Xavier ^a   Pons, Josep M ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034345655     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1289825     Document Type: Article

References (26)

1. P. J. Olver, Applications of Lie Groups to Differential Equations, 2nd ed. (Springer, New York, 1993).
2. R. Abraham and J. E. Marsden, Foundations of Mechanics, 2nd ed. (Addison-Wesley, Reading, 1978).
3. V. I. Arnol'd, Mathematical Methods of Classical Mechanics, 2nd ed. (Springer-Verlag, New York, 1989).
4. P. A. M. Dirac, "Generalized Hamiltonian dynamics," Can. J. Math. 2, 129-148 (1950).
5. P. A. M. Dirac, Lectures on Quantum Mechanics (Yeshiva University Press, New York, 1964).
6. C. Batlle, J. Gomis, J. M. Pons, and N. Roman, "Equivalence between the Lagrangian and Hamiltonian formalisms for constrained systems," J. Math. Phys. 27, 2953-2962 (1986).
7. J. F. Cariñena, "Theory of singular Lagrangians," Fortschr. Phys. 38, 641-679 (1990).
8. G. Marmo, N. Mukunda, and J. Samuel, "Dynamics and symmetry for constrained systems: a geometrical analysis," Riv. Nuovo Cimento 6, 1-62 (1983).
9. A. Hanson, T. Regge, and C. Teitelboim, Constrained Hamiltonian Systems, (Accademia Nazionale dei Lincei, Roma, 1976).
10. X. Gràcia and J. M. Pons, "Gauge generators, Dirac's conjecture, and degrees of freedom for constrained systems," Ann. Phys. (N.Y.) 187, 355-368 (1988).
11. X. Gràcia and J. M. Pons, "Noether transformations with vanishing conserved quantity," Ann. Inst. Henri Poincaré, Sect. A 61, 315-327 (1994).
12. K. Kamimura, "Singular Lagrangian and constrained Hamiltonian systems, generalized canonical formalism," Nuovo Cimento Soc. Ital. Fis., B 68, 33-54 (1982).
13. X. Gràcia and J. M. Pons, "A Hamiltonian approach to Lagrangian Noether transformations," J. Phys. A 25, 6357-6369 (1992).
14. X. Gràcia and J. Roca, "Covariant and noncovariant gauge transformations for the conformal particle," Mod. Phys. Lett. A 8, 1747-1761 (1993).
15. J. A. García and J. M. Pons, "Rigid and gauge Noether symmetries for constrained systems," Int. J. Mod. Phys. A (to be published), hep-th/9908151.
16. 2 model," J. Math. Phys. 30, 1345-1350 (1989).
17. X. Gràcia and J. M. Pons, "On an evolution operator connecting Lagrangian and Hamiltonian formalisms," Lett. Math. Phys. 17, 175-180 (1989).
18. J. M. Pons, "New relations between Hamiltonian and Lagrangian constraints," J. Phys. A 21, 2705-2715 (1988).
19. X. Gràcia, "Fibre derivatives: some applications to singular lagrangians," Rep. Math. Phys. 45, 67-84 (2000).
20. X. Gràcia and J. M. Pons, "Singular lagrangians: Some geometric structures along the Legendre's map" (submitted).
21. M. J. Gotay, J. M. Nester, and G. Hinds, "Presymplectic manifolds and the Dirac-Bergmann theory of constraints," J. Math. Phys. 19, 2388-2399 (1978).
22. M. J. Bergvelt and E. A. de Kerf, "The Hamiltonian structure of Yang-Mills theories and instantons I," Physica A 139, 101-124 (1986).
23. I. A. Batalin, "Quasigroup construction and first class constraints," J. Math. Phys. 22, 1837-1850 (1981).
24. J. M. Pons, D. C. Salisbury, and L. C. Shepley, "Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant systems," Phys. Rev. D 55, 658-668 (1997), gr-qc/9612037.
25. J. M. Pons, D. C. Salisbury, and L. C. Shepley, "Gauge transformations in Einstein-Yang-Mills theories," J. Math. Phys. 41, 5557-5571 (2000), gr-qc/9912086.
26. J. M. Pons, D. C. Salisbury, and L. C. Shepley, "Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity," Phys. Rev. D (to be published), gr-qc/9912085.