Advertisement

Hamiltonian Quantization with Constraints

Chapter
  • 617 Downloads

Abstract

In the framework of the Dirac quantization with the second class constraints, a free particle moving on surface of (d − 1)-dimensional sphere has ambiguity in its energy spectrum due arbitrary shift of canonical momenta. In this chapter, we show that this spectrum obtained by the Dirac method can be consistent with that of the improved Dirac Hamiltonian formalism at the level of the first class constraint by fixing ambiguity, and then we discuss its physical consequences [48]. We next study a free particle system residing on torus to investigate its first class Hamiltonian associated with its Stückelberg coordinates [56].

Keywords

Hamiltonian Quantization Class Constraints Dirac Method Free Particle Dirac Brackets 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 4.
    B. De Witt, Rev. Mod. Phys. 29, 377 (1957)CrossRefADSMathSciNetGoogle Scholar
  2. 6.
    H. Dekker, Physica A 103, 586 (1980)CrossRefADSMathSciNetGoogle Scholar
  3. 11.
    P. Dita, Phys. Rev. A 56, 2574 (1997)CrossRefADSGoogle Scholar
  4. 13.
    E. Abdalla, R. Banerjee, Braz. J. Phys. 31, 80 (2001)CrossRefADSGoogle Scholar
  5. 14.
    P.A.M. Dirac, Lectures in Quantum Mechanics (Yeshiva University, New York, 1964)Google Scholar
  6. 15.
    I.A. Batalin, E.S. Fradkin, Phys. Lett. B 180, 157 (1986)CrossRefADSMathSciNetGoogle Scholar
  7. 22.
    A.J. Niemi, Phys. Lett. B 213, 41 (1988)CrossRefADSMathSciNetGoogle Scholar
  8. 27.
    R. Banerjee, Phys. Rev. D 48, R5467 (1993)CrossRefADSGoogle Scholar
  9. 42.
    S.T. Hong, Y.W. Kim, Y.J. Park, Phys. Rev. D 59, 114026 (1999)CrossRefADSMathSciNetGoogle Scholar
  10. 48.
    S.T. Hong, W.T. Kim, Y.J. Park, Mod. Phys. Lett. A 15, 1915 (2000)CrossRefADSzbMATHMathSciNetGoogle Scholar
  11. 56.
    S.T. Hong, Mod. Phys. Lett. A 20, 1577 (2005)CrossRefADSzbMATHGoogle Scholar
  12. 75.
    W. Oliveira, J.A. Neto, Int. J. Mod. Phys. A 12, 4895 (1997)CrossRefADSzbMATHMathSciNetGoogle Scholar
  13. 97.
    S.T. Hong, Mod. Phys. Lett. A 20, 1577 (2005)CrossRefADSzbMATHGoogle Scholar
  14. 135.
    J.A. Neto, J. Phys. G 21, 695 (1995)CrossRefADSGoogle Scholar
  15. 136.
    J.A. Neto, W. Oliveira, Int. J. Mod. Phys. A 14, 3699 (1999)CrossRefADSzbMATHMathSciNetGoogle Scholar
  16. 137.
    K. Fujii, N. Ogawa, Prog. Theor. Phys. Suppl. 109, 1 (1992)CrossRefADSMathSciNetGoogle Scholar
  17. 138.
    T.D. Lee, Particle Physics and Introduction to Field Theory (Harwood, New York, 1981)Google Scholar
  18. 139.
    N. Vilenkin, Special Functions and the Theory of Group Representations (American Mathematical Society, Providence, 1968)zbMATHGoogle Scholar
  19. 140.
    P.M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Science EducationEwha Womans UniversitySeoulRepublic of Korea

Personalised recommendations