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Introduction

Chapter
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Abstract

It is well known that canonical quantization of a free point particle in curved space is a long standing and controversial problem in quantum mechanics [1–13]. Indeed, for such system, correspondence of classical mechanics and quantum one does not uniquely define Hamiltonian operator and this ambiguity affects an energy spectrum of the physical system. In order to quantize rigorously physical systems subjected to constraints, Dirac Hamiltonian scheme [14] has been widely used in theoretical physics: it has appeared from string theory to produce Virasoro conditions, to nuclear phenomenology. However, the resulting Dirac brackets may be field dependent and nonlocal, and thus pose serious ordering problems for the quantization of the theory. In order to avoid this problem, the improved Dirac Hamiltonian scheme converting the second class constraints into first class ones has been developed [15–22] and it restricts quantum mechanical Hilbert space instead of configuration space. The operators representing the first class constraints are then generators of gauge transformations, and the physical states are all found by going into gauge invariant subspace of the Hilbert space.

Keywords

Class Constraint Skyrmion Model Linear Sigma Model Baryon Decuplet Strange Form Factor 
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. 1.
    B. Podolsky, Phys. Rev. 32, 812 (1928)CrossRefADSzbMATHGoogle Scholar
  2. 13.
    E. Abdalla, R. Banerjee, Braz. J. Phys. 31, 80 (2001)CrossRefADSGoogle Scholar
  3. 14.
    P.A.M. Dirac, Lectures in Quantum Mechanics (Yeshiva University, New York, 1964)Google Scholar
  4. 15.
    I.A. Batalin, E.S. Fradkin, Phys. Lett. B 180, 157 (1986)CrossRefADSMathSciNetGoogle Scholar
  5. 19.
    L.D. Faddeev, S.L. Shatashvili, Phys. Lett. B 167, 225 (1986)CrossRefADSGoogle Scholar
  6. 21.
    K. Harada, I. Tsutsui, Phys. Lett. B 183, 311 (1987)CrossRefADSGoogle Scholar
  7. 22.
    A.J. Niemi, Phys. Lett. B 213, 41 (1988)CrossRefADSMathSciNetGoogle Scholar
  8. 23.
    T. Fujiwara, Y. Igarashi, J. Kubo, Nucl. Phys. B 341, 695 (1990)CrossRefADSzbMATHMathSciNetGoogle Scholar
  9. 26.
    Y.W. Kim, S.K. Kim, W.T. Kim, Y.J. Park, K.Y. Kim, Y. Kim, Phys. Rev. D 46, 4574 (1992)CrossRefADSMathSciNetGoogle Scholar
  10. 42.
    S.T. Hong, Y.W. Kim, Y.J. Park, Phys. Rev. D 59, 114026 (1999)CrossRefADSMathSciNetGoogle Scholar
  11. 43.
    S.T. Hong, W.T. Kim, Y.J. Park, Phys. Rev. D 60, 125005 (1999)CrossRefADSMathSciNetGoogle Scholar
  12. 45.
    S.T. Hong, W.T. Kim, Y.J. Park, M.S. Yoon, Phys. Rev. D 62, 085010 (2000)CrossRefADSMathSciNetGoogle Scholar
  13. 47.
    S.T. Hong, Y.J. Park, Mod. Phys. Lett. A 15, 913 (2000)CrossRefADSMathSciNetGoogle Scholar
  14. 49.
    D.K. Hong, S.T. Hong, Y.J. Park, Phys. Lett. B 499, 125 (2001)CrossRefADSzbMATHGoogle Scholar
  15. 50.
    S.T. Hong, Y.J. Park, Phys. Rev. D 63, 054018 (2001)CrossRefADSMathSciNetGoogle Scholar
  16. 53.
    S.T. Hong, S.H. Lee, Eur. Phys. J. C 25, 131 (2002)CrossRefADSGoogle Scholar
  17. 54.
    S.T. Hong, A.J. Niemi, Phys. Rev. D 72, 127701 (2005)CrossRefADSMathSciNetGoogle Scholar
  18. 55.
    S.T. Hong, Phys. Lett. A 348, 82 (2006)CrossRefADSzbMATHMathSciNetGoogle Scholar
  19. 58.
    S.T. Hong, Y.J. Park, Phys. Rep. 358, 143 (2002)CrossRefADSzbMATHGoogle Scholar
  20. 59.
    J. Wess, B. Zumino, Phys. Lett. B 37, 95 (1971)CrossRefADSMathSciNetGoogle Scholar
  21. 60.
    L. Faddeev, R. Jackiw, Phys. Rev. Lett. 60, 1692 (1988)CrossRefADSzbMATHMathSciNetGoogle Scholar
  22. 62.
    R. Jackiw, Diverse Topics in Theoretical and Mathematical Physics (World Scientific, Singapore, 1995)CrossRefzbMATHGoogle Scholar
  23. 63.
    J. Barcelos-Neto, C. Wotzasek, Mod. Phys. Lett. A 7, 1172 (1992)CrossRefMathSciNetGoogle Scholar
  24. 68.
    Y.W. Kim, Y.J. Park, K.Y. Kim, Y. Kim, J. Korean Phys. Soc. 27, 610 (1994)Google Scholar
  25. 70.
    S.T. Hong, Y.W. Kim, Y.J. Park, K.D. Rothe, Mod. Phys. Lett. A 17, 435 (2002)CrossRefADSzbMATHMathSciNetGoogle Scholar
  26. 72.
    S.T. Hong, Y.W. Kim, Y.J. Park, K.D. Rothe, J. Phys. A 36, 1643 (2003)CrossRefADSzbMATHMathSciNetGoogle Scholar
  27. 73.
    S.T. Hong, Mod. Phys. Lett. A 20, 2455 (2005)CrossRefADSzbMATHGoogle Scholar
  28. 74.
    A.C.R. Mendes, J.A. Neto, W. Oliveira, C. Neves, D.C. Rodrigues, hep-th/0109089Google Scholar
  29. 75.
    W. Oliveira, J.A. Neto, Int. J. Mod. Phys. A 12, 4895 (1997)CrossRefADSzbMATHMathSciNetGoogle Scholar
  30. 76.
    C. Becchi, A. Rouet, R. Stora, Phys. Lett. B 52, 344 (1974)CrossRefADSGoogle Scholar
  31. 78.
    I.V. Tyutin, Levedev preprint, LEBEDEV-75-39 (1975)Google Scholar
  32. 79.
    E.S. Fradkin, G.A. Vilkovisky, Phys. Lett. B 55, 224 (1975)CrossRefADSzbMATHMathSciNetGoogle Scholar
  33. 82.
    S. Hamamoto, Prog. Theor. Phys. 95, 441 (1996)CrossRefADSMathSciNetGoogle Scholar
  34. 83.
    F. Wilczek, A. Zee, Phys. Rev. Lett. 51, 2250 (1983)CrossRefADSMathSciNetGoogle Scholar
  35. 86.
    G.W. Semenoff, Phys. Rev. Lett. 61, 517 (1988)CrossRefADSMathSciNetGoogle Scholar
  36. 87.
    M.B. Green, J.H. Schwarz, E. Witten, Superstring Theory (Cambridge University Press, Cambridge, 1987)zbMATHGoogle Scholar
  37. 88.
    J. Polchinski, String Theory (Cambridge University Press, Cambridge, 1998)CrossRefGoogle Scholar
  38. 89.
    E. Witten, Phys. Rev. D 46, 5467 (1992)CrossRefADSMathSciNetGoogle Scholar
  39. 90.
    K. Hotta, JHEP 0309, 002 (2003)CrossRefADSMathSciNetGoogle Scholar
  40. 91.
    J.J. Atick, E. Witten, Nucl. Phys. B 310, 291 (1988)CrossRefADSMathSciNetGoogle Scholar
  41. 92.
    S.S. Gubser, S. Gukov, I.R. Klebanov, M. Rangamani, E. Witten, J. Math. Phys. 42, 2749 (2001)CrossRefADSzbMATHMathSciNetGoogle Scholar
  42. 93.
    M. Aguado, M. Asorey, A. Wipf, Ann. Phys. 298, 2 (2002)CrossRefADSzbMATHMathSciNetGoogle Scholar
  43. 94.
    E.B. Bogomolny, Sov. J. Nucl. Phys. 24, 449 (1976)Google Scholar
  44. 95.
    M.K. Prasad, C.M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975)CrossRefADSGoogle Scholar
  45. 96.
    K.L. Chan, M. Cvetic, Phys. Lett. B 375, 98 (1996)CrossRefADSzbMATHMathSciNetGoogle Scholar
  46. 97.
    S.T. Hong, Mod. Phys. Lett. A 20, 1577 (2005)CrossRefADSzbMATHGoogle Scholar
  47. 98.
    C. Carathéodory, Calculus of Variations and Partial Differential Equations of First Order (American Mathematical Society, Providence, 1999)Google Scholar
  48. 99.
    H.A. Kastrup, Phys. Rep. 101, 1 (1983)CrossRefADSMathSciNetGoogle Scholar
  49. 100.
    Y. Güler, J. Math. Phys. 30, 785 (1989)CrossRefADSzbMATHMathSciNetGoogle Scholar
  50. 101.
    B.M. Pimentel, R.G. Teixeira, J.L. Tomazelli, Ann. Phys. 267, 75 (1998)CrossRefADSzbMATHMathSciNetGoogle Scholar
  51. 104.
    S.T. Hong, W.T. Kim, Y.W. Kim, Y.J. Park, J. Korean Phys. Soc. 43, 981 (2003)Google Scholar
  52. 105.
    D. Dominici, J. Gomis, G. Longhi, J.M. Pons, J. Math. Phys. 25, 2439 (1984)CrossRefADSzbMATHMathSciNetGoogle Scholar
  53. 106.
    D.B. Kaplan, A.E. Nelson, Phy. Lett. B 175, 57 (1986)CrossRefADSGoogle Scholar
  54. 107.
    G.E. Brown, K. Kubodera, M. Rho, Phys. Lett. B 192, 273 (1987)CrossRefADSGoogle Scholar
  55. 108.
    H.D. Politzer, M.B. Wise, Phys. Lett. B 273, 156 (1991)CrossRefADSGoogle Scholar
  56. 109.
    H. Yabu, S. Nakamura, F. Myhrer, K. Kubodera, Phys. Lett. B 315, 17 (1993)CrossRefADSGoogle Scholar
  57. 110.
    M. Alford, K. Rajagopal, F. Wilczek, Nucl. Phys. B 537, 443 (1999)CrossRefADSGoogle Scholar
  58. 111.
    M. Stone, Bosonization (World Scientific, Singapore, 1994)CrossRefGoogle Scholar
  59. 112.
    L.D. Faddeev, A.J. Niemi, Phys. Rev. Lett. 82, 1624 (1999)CrossRefADSzbMATHMathSciNetGoogle Scholar
  60. 113.
    E. Babaev, L.D. Faddeev, A.J. Niemi, Phys. Rev. B 65, 100512 (2002)CrossRefADSGoogle Scholar
  61. 114.
    L.D. Faddeev, A.J. Niemi, Nature 387, 58 (1997)CrossRefADSGoogle Scholar
  62. 115.
    E. Witten, Nucl. Phys. B 223, 422 (1983)CrossRefADSMathSciNetGoogle Scholar
  63. 117.
    P.O. Mazur, M.A. Nowak, M. Praszalowicz, Phys. Lett. B 147, 137 (1984)CrossRefADSMathSciNetGoogle Scholar
  64. 118.
    S.T. Hong, B.Y. Park, Nucl. Phys. A 561, 525 (1993)CrossRefGoogle Scholar
  65. 120.
    S.T. Hong, G.E. Brown, Nucl. Phys. A 580, 408 (1994)CrossRefADSGoogle Scholar
  66. 121.
    H. Yabu, K. Ando, Nucl. Phys. B 301, 601 (1988)CrossRefADSGoogle Scholar
  67. 122.
    J.H. Kim, C.H. Lee, H.K. Lee, Nucl. Phys. A 501, 835 (1989)CrossRefADSGoogle Scholar
  68. 123.
    H.K. Lee, D.P. Min, Phys. Lett. B 219, 1 (1989)CrossRefADSGoogle Scholar
  69. 124.
    C.G. Callan, I. Klebanov, Nucl. Phys. B 262, 365 (1985)CrossRefADSGoogle Scholar
  70. 125.
    N.N. Scoccola, H. Nadeau, M.A. Nowak, M. Rho, Phys. Lett. B 201, 425 (1988)CrossRefADSGoogle Scholar
  71. 126.
    K.M. Westerberg, I.R. Klebanov, Phys. Rev. D 50, 5834 (1994)CrossRefADSGoogle Scholar
  72. 127.
    I.R. Klebanov, K.M. Westerberg, Phys. Rev. D 53, 2804 (1996)CrossRefADSGoogle Scholar
  73. 128.
    S.T. Hong, J. Lee, T.H. Lee, P. Oh, Phys. Rev. D 68, 065022 (2003)CrossRefADSMathSciNetGoogle Scholar
  74. 129.
    S.T. Hong, Nucl. Phys. A 721, 421 (2003)CrossRefADSGoogle Scholar
  75. 130.
    S.T. Hong, Phys. Lett. B 585, 122 (2004)CrossRefADSGoogle Scholar
  76. 131.
    S.T. Hong, Phys. Rev. D 76, 094029 (2007)CrossRefADSGoogle Scholar
  77. 132.
    G. ’t Hooft, Nucl. Phys. B 79, 276 (1974)Google Scholar
  78. 133.
    A.M. Polyakov, JETP Lett. 20, 194 (1974)ADSGoogle Scholar
  79. 134.
    S.T. Hong, Mod. Phys. Lett. A 25, 2529 (2010)CrossRefADSzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Science EducationEwha Womans UniversitySeoulRepublic of Korea

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