HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 60 (1978) > Number 6
| Next Article >

Prog. Theor. Phys. Vol. 60 No. 6 (1978) pp. 1869-1889

[ Full Text PDF : FREE ACCESS (1714K) ]

Manifestly Covariant Canonical Formulation of the Yang-Mills Field Theories. I

— General Formalism —

Taichiro Kugo and Izumi Ojima*

Department of Physics, Kyoto University, Kyoto 606
*Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606

(Received July 7, 1978)

Abstract:

A canonical formalism of the Yang-Mills theories is presented in the framework of manifestly covariant quantum field theory, which is found to give a natural extension of the Gupta-Bleuler formalism. Physical states are defined by the two subsidiary conditions QB|phys >= QC|phys >= 0, where the conserved charges QB and QC are the generators of the Becchi-Rouet-Stora transformation and of the Faddeev-Popov ghost scale transformation, respectively. With the aid of the explicit expressions of QB and QC in terms of the asymptotic fields, it is proved that the physical state conditions are satisfied and, as a consequence, the physical S-matrix is unitary. It is emphasized that the Faddeev-Popov ghosts c and c should be hermitian (i.e., c† = c, c = c†) in order for the Lagrangian L and the charges QB and QC to be hermitian. Only with this unconventional assignment, one can achieve a transparent and consistent formulation of the Yang-Mills theories. The structures of the total state vector space and of the physical subspace are clarified based on the detailed analysis of the asymptotic fields given in the present series of papers.


URL : http://ptp.ipap.jp/link?PTP/60/1869/
DOI : 10.1143/PTP.60.1869

[ Full Text PDF : FREE ACCESS (1714K) ] Citation:

References:

  1. G. 't Hooft, Nucl. Phys. B 33 (1971), 173[CrossRef]; ibid. 35 (1971), 167[CrossRef].
    G. 't Hooft and M. Veltman, Nucl. Phys. B 50 (1972), 318[CrossRef].
    B. W. Lee and J. Zinn-Justin, Phys. Rev. D 5 (1973), 3121[APS]; ibid. 5 (1973), 3137[APS]; ibid. 5 (1973), 3155[APS]; ibid. 7 (1973), 1049[APS].
  2. T. Kugo and I. Ojima, Phys. Lett. B 73 (1978), 459[CrossRef].
  3. N. Nakanishi, Prog. Theor. Phys. 35 (1966), 1111[PTP]; ibid. 49 (1973), 640[PTP]; ibid. 52 (1974), 1929[PTP].
    B. Lautrup, Kgl. Danske Videnskab. Selskab, Mat.-fys. Medd. 35 (1967), No. 11, 1.
  4. S. N. Gupta, Proc. Phys. Soc. A 63 (1950), 681.
    K. Bleuler, Helv. Phys. Acta 23 (1950), 567.
  5. E. Rudoph and H. P. Dürr, Nuovo Cim. A 10 (1972), 597.
  6. C. Becchi, A. Rouet and R. Stora, Ann. of Phys. 98 (1976), 287[CrossRef].
  7. G. Curci and R. Ferrari, Nuovo Cim. A 35 (1976), 273.
  8. T. Kugo and I. Ojima, Prog. Theor. Phys. 61 (1979), 294[PTP].
  9. F. A. Berezin, The Method of Second Quantization (Academic Press, New York, 1966).
  10. G. 'tHooft, Nucl. Phys. B 35 (1971), 167[CrossRef].
  11. J. Zinn-Justin, “Renormalization of Gauge Theories”, in Lecture Notes in Physics, Vol. 37 (Springer, Berlin, 1975).
  12. K. L. Nagy, State Vector Space with Indefinite Metric in Quantum Field Theory (P. Noordhoff, Groningen, 1966).
    N. Nakanishi, Prog. Theor. Phys. Suppl. No. 51 (1972), 1, [PTP]and references cited therein.
  13. O. W. Greenberg, J. Math. Phys. 3 (1962), 859[CrossRef].
    D. W. Robinson, Helv. Phys. Acta 35 (1962), 403.
    G. F. Dell'Antonio, J. Math. Phys. 2 (1961), 759[CrossRef].
    Applicability of this theorem to the case with an indefinite metric was commented in:
    N. Nakanishi and I. Ojima, Prog. Theor. Phys. 59 (1978), 242[PTP].
  14. V. Glaser, H. Lehmann and W. Zimmermann, Nuovo Cim. 6 (1957), 1122.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 61 No. 1 (1979) pp. 294-314 :
    Manifestly Covariant Canonical Formulation of Yang-Mills Field Theories. II
    Taichiro Kugo and Izumi Ojima
  2. Progress of Theoretical Physics Vol. 61 No. 2 (1979) pp. 644-655 :
    Manifestly Covariant Canonical Formulation of Yang-Mills Field Theories. III
    Taichiro Kugo and Izumi Ojima
  3. Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 305-307 :
    Covariant Canonical Quantization of Massless Rarita-Schwinger Field
    Masanori Okawa
  4. Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 779-792 :
    Indefinite-Metric Quantum Field Theory of General Relativity. V
    Noboru Nakanishi
  5. Progress of Theoretical Physics Vol. 62 No. 5 (1979) pp. 1396-1402 :
    On the General Validity of the Unitarity Proof in the Kugo-Ojima Formalism of Gauge Theories
    Noboru Nakanishi
  6. Progress of Theoretical Physics Vol. 63 No. 4 (1980) pp. 1364-1383 :
    Non-Trivial Realization of the BRS Supersymmetry
    Kazuo Fujikawa
  7. Progress of Theoretical Physics Vol. 63 No. 6 (1980) pp. 2061-2077 :
    The Higgs-Kibble Model on the Basis of a Canonical Yang-Mills Field Theory with Gauge Covariance. I
    Takashi Fukuda and Kan-ichi Yokoyama
  8. Progress of Theoretical Physics Vol. 64 No. 4 (1980) pp. 1395-1411 :
    The Form of BRS-Invariant Operators
    Taichiro Kugo and Shozo Uehara
  9. Progress of Theoretical Physics Vol. 64 No. 4 (1980) pp. 1412-1424 :
    Gauge Covariance in Non-Abelian Gauge Theories
    Kan-ichi Yokoyama, Minoru Takeda and Minoru Monda
  10. Progress of Theoretical Physics Vol. 65 No. 6 (1981) pp. 2023-2037 :
    On Quantum Theory of General-Relativistic Many-Particle Systems. I
    Ikuo Ichinose
  11. Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1827-1842 :
    Quantum Theory of Massive Yang-Mills Fields. I
    Takashi Fukuda, Minoru Monda, Minoru Takeda and Kan-ichi Yokoyama
  12. Progress of Theoretical Physics Vol. 67 No. 4 (1982) pp. 1206-1215 :
    Quantum Theory of Massive Yang-Mills Fields. II
    Takashi Fukuda, Minoru Monda, Minoru Takeda and Kan-ichi Yokoyama
  13. Progress of Theoretical Physics Vol. 67 No. 5 (1982) pp. 1607-1618 :
    Restoration of the Local Gauge Symmetry and Color Confinement in Non-Abelian Gauge Theories
    Hiroyuki Hata
  14. Progress of Theoretical Physics Vol. 113 No. 1 (2005) pp. 199-213 :
    4D Equivalence Theorem and Gauge Symmetry on an Orbifold
    Yoshikazu Abe, Naoyuki Haba, Katsuhiro Hayakawa, Yasunori Matsumoto, Mamoru Matsunaga and Kenta Miyachi
  15. Progress of Theoretical Physics Vol. 117 No. 4 (2007) pp. 695-713 :
    BRST Symmetric Gaugeon Formalism for the Higgs Model
    Hikaru Miura and Ryusuke Endo
  16. Progress of Theoretical Physics Vol. 121 No. 5 (2009) pp. 1125-1131 :
    Dynamical Gauged S-Duality Spontaneous Breakdown
    Eiji Konishi
  17. Progress of Theoretical Physics Supplement No.66 (1979) pp. 1-130 :
    Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem
    Taichiro Kugo and Izumi Ojima
  18. Progress of Theoretical Physics Supplement No.111 (1993) pp. 1-41 :
    Basic Ideas of Stochastic Quantization
    Mikio Namiki
  19. Progress of Theoretical Physics Supplement No.114 (1993) pp. 97-107 :
    Effective Action Approach to Two-Dimensional Quantum Gravity
    Shoichi Ichinose

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.