Advertisement

International Journal of Theoretical Physics

, Volume 47, Issue 9, pp 2319–2325 | Cite as

Total Hamiltonian and Extended Hamiltonian for Constrained Hamilton Systems

  • Yong-Long Wang
  • Chuan-Cong Wang
  • Xue-Feng Ning
  • Shu-Tao Ai
  • Hong-Zhe Pan
  • Tong-Song Jiang
Article
  • 136 Downloads

Abstract

For constrained Hamiltonian systems, the motion equations are deduced from total Hamiltonian and extended Hamiltonian with Lagrangian multipliers depending on time t and canonical variables q i and p i . When the multipliers reduced to only depend on time t, the motion equations exactly agree with the old results. Under the same conditions (Lagrangian multipliers depend on time t and canonical variables q i and p i ), the relation equations of coefficients in the generator of gauge transformation are deduced, but the equations have an additive term besides the well-known results. This additive term is from Lagrangian multipliers depending on canonical variables, and it might perform the gauge symmetries that needs to be discussed further.

Keywords

Constrained Hamiltonian system Total Hamiltonian Extended Hamiltonian Canonical Hamiltonian equations Gauge symmetry 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dirac, P.A.M.: Can. J. Math. 2, 129 (1950) MATHMathSciNetGoogle Scholar
  2. 2.
    Dirac, P.A.M.: Lecture on Quantum Mechanics. Yeshiva University, New York (1964) Google Scholar
  3. 3.
    Gitman, D.M., Tyutin, I.V.: Quantization of Field with Constraints. Springer, Berlin (1990) Google Scholar
  4. 4.
    Anderson, J.L., Bergmann, P.G.: Phys. Rev. 83, 1018 (1951) MATHCrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Bergmann, P.G., Goldberg, J.: Phys. Rev. 98, 531 (1955) MATHCrossRefADSMathSciNetGoogle Scholar
  6. 6.
    Kamimura, K.: Nuovo Cimento B 68, 33 (1962) CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Shanmugadahasan, S.: Proc. Camb. Phil. Soc. 59, 743 (1963) CrossRefGoogle Scholar
  8. 8.
    Shanmugadahasan, S.: J. Math. Phys. 14, 677 (1973) CrossRefADSGoogle Scholar
  9. 9.
    Sudarshan, E., Mukunda, N.: Classical Dynamics, A Modern Perspective. Wiley, New York (1974) MATHGoogle Scholar
  10. 10.
    Henneaux, M., Teitelboim, C.: Quantization of Gauge System. Princeton University Press, Princeton (1992) Google Scholar
  11. 11.
    Cabo, A.: J. Phys. A: Gen. 19, 629 (1986) CrossRefADSMathSciNetMATHGoogle Scholar
  12. 12.
    Costa, M.E.V., Girotti, H.O., Simoes, T.J.M.: Phys. Rev. D 32, 405 (1985) CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Li, A.M., Jiang, J.H., Li, Z.P.: Acta Phys. Sin. 51, 945 (2002) MathSciNetGoogle Scholar
  14. 14.
    Li, Z.P., Li, A.M., Jiang, J.H., Wang, Y.L.: Comm. Theor. Phys. 43, 1115 (2005) MathSciNetGoogle Scholar
  15. 15.
    Shirzad, A.: J. Phys. A: Gen. 31, 2747 (1998) MATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Banerjee, R., Rothe, H.J., Rothe, K.D.: Phys. Lett. B 463, 248 (1999) MATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Banerjee, R., Rothe, H.J., Rothe, K.D.: J. Phys. A: Gen. 33, 2059 (2000) MATHCrossRefADSMathSciNetGoogle Scholar
  18. 18.
    Rothe, H.J., Rothe, K.D.: J. Phys. A: Gen. 36, 1671 (2003); hep-th/0302210 MATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Rothe, H.J., Rothe, K.D.: Ann. Phys. 313, 479 (2004) MATHCrossRefADSMathSciNetGoogle Scholar
  20. 20.
    Rothe, H.J.: Phys. Lett. B 539, 296 (2002) MATHCrossRefADSMathSciNetGoogle Scholar
  21. 21.
    Rothe, H.J.: Phys. Lett. B 569, 90 (2003) MATHCrossRefADSMathSciNetGoogle Scholar
  22. 22.
    Banerjee, R., Rothe, H.J., Rothe, K.D.: Phys. Lett. B 479, 429 (2000) MATHCrossRefADSMathSciNetGoogle Scholar
  23. 23.
    Galvão, C.A.P., Boechat, J.B.T.: J. Math. Phys. 30, 1122 (1990) Google Scholar
  24. 24.
    Wang, Y.L., Li, Z.P.: Rediscussion of Gauge Symmetry (in preparation) Google Scholar
  25. 25.
    Qi, Z.: Int. J. Theor. Phys. 29, 1309 (1990) CrossRefGoogle Scholar
  26. 26.
    Li, Z.P., Li, X.: Int. J. Theor. Phys. 30, 225 (1991) MATHCrossRefGoogle Scholar
  27. 27.
    Li, Z.P., Li, X.: Phys. Rev. E 52, 876 (1994) CrossRefADSGoogle Scholar
  28. 28.
    Cawley, R.: Phys. Rev. Lett. 42, 413 (1979) CrossRefADSGoogle Scholar
  29. 29.
    Cawley, R.: Phys. Rev. D 21, 2988 (1980) CrossRefADSGoogle Scholar
  30. 30.
    Li, Z.P.: Chin. Phys. Lett. 10, 68 (1993) Google Scholar
  31. 31.
    Li, Z.P.: Europhys. Lett. 21, 141 (1993) CrossRefADSGoogle Scholar
  32. 32.
    Li, Z.L., Jiang, J.H.: Symmetries in Constrained Canonical Systems. Science Press, Beijing (2002) Google Scholar
  33. 33.
    Li, Z.P.: Classical and Quantal Dynamics of Constrained Systems and Their Symmetry Properties. Beijing Polytechnic University Press, Beijing (1993) (in Chinese) Google Scholar
  34. 34.
    Li, Z.P.: Constrained Hamiltonian Systems and Their Symmetry Properties. Beijing Polytechnic University Press, Beijing (1999) (in Chinese) Google Scholar
  35. 35.
    Li, Z.P.: J. Phys. A: Gen. 24, 426 (1991) ADSGoogle Scholar
  36. 36.
    Li, Z.P.: High Energy Phys. Nucl. Phys. 17, 693 (1994) (in Chinese) ADSGoogle Scholar
  37. 37.
    Wang, A.M., Ruan, T.N.: Phys. Rev. Lett. 73, 2011 (1994) MATHCrossRefADSMathSciNetGoogle Scholar
  38. 38.
    Wang, A.M., Ruan, T.N.: Phys. Rev. A 54, 57 (1996) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Yong-Long Wang
    • 1
    • 2
  • Chuan-Cong Wang
    • 1
  • Xue-Feng Ning
    • 1
  • Shu-Tao Ai
    • 1
  • Hong-Zhe Pan
    • 1
  • Tong-Song Jiang
    • 2
  1. 1.Institute of Condensed Matter of PhysicsLinyi Normal UniversityLinyiChina
  2. 2.Institute of Applied MathematicsLinyi Normal UniversityLinyiChina

Personalised recommendations