Variational methods in the master field formulation for (3+1)-dimensional quantum chromodynamics

Masa-aki Sato

doi:10.1103/PhysRevD.29.2952

Access by Xinjiang University

Variational methods in the master field formulation for (3+1)-dimensional quantum chromodynamics

Masa-aki Sato

Department of Physics, New York University, 4 Washington Place, New York, New York 10003

PDF

Phys. Rev. D 29, 2952 – Published 15 June, 1984

DOI: https://doi.org/10.1103/PhysRevD.29.2952

Abstract

Master fields are formulated for finite- $N$ (3+1)-dimensional QCD. They satisfy classical Yang-Mills equations with an infinite number of internal indices and an infinite number of constraints. Master fields and constraints on them in the large- $N$ limit ( $N \to \infty$ with fixed $g^{2} N$ ) are derived from the finite- $N$ master fields and constraints using vacuum dominance among color-singlet states. Explicit solutions for the large- $N$ constraints are given and used as trial functions in a Hartree-Fock variational calculation. This Hartree-Fock method can include essential features of gluon condensation effects in the QC $D_{3 + 1}$ vacuum which is expected to cause confinement. Inclusion of quark fields and Hartree-Fock equations for the meson energy spectrum are also discussed.

References (17)

M. Sato, Phys. Lett. 113B, 315 (1982)
S. Mandelstam, Phys. Rev. D 19, 2391 (1979) R. Giles, 24, 2160 (1981)
G. 't Hooft, Nucl. Phys. B72, 461 (1974) E. Witten, ibid. B160, 57 (1979) S. Coleman, in The Whys of Subnuclear Physics, proceedings of the International School of Subnuclear Physics, Erice, 1977, edited by A. Zichichi (Plenum, New York, 1979)
K. Bardakci, Nucl. Phys. B178, 263 (1981) ibid.B193, 245 (1981) M. B. Halpern, ibid. B188, 61 (1981) M. B. Halpern and C. Schwartz, Phys. Rev. D 24, 2146 (1981)
R. Fukuda, Phys. Lett. 73B, 33 (1978) Phys. Rev. D 21, 485 (1980)
J. Kogut and L. Susskind, Phys. Rev. D 9, 3501 (1974) G. 't Hooft, in Recent Progress in Lagrangian Field Theory and Applications, proceedings of the Marseilles Colloquium, 1974, edited by C. P. Korthes-Altes (Centre de Physique Theorique, Marseilles, 1975)
J. Sakamoto and M. Sato, Prog. Theor. Phys. 56, 1617 (1976) R. Utiyama and J. Sakamoto, ibid. 55, 1631 (1976) E. S. Fradkin and I. V. Tyutin, Phys. Rev. D 2, 2841 (1970)
V. N. Gribov, lecture at the 12th Winter School of the Leningrad Nuclear Physics Institute, 1977 (unpublished)
T. Kugo and I. Ojima, Suppl. Progr. Theor. Phys. 66, 1 (1979)
N. N. Bogoliubov, Zh. Eksp. Teor. Fiz. 34, [Sov. Phys. JETP 7, 41 (1958)]
I. Bars and M. B. Green, Phys. Rev. D 17, 537 (1978)
C. G. Callan, N. Coote, and D. J. Gross, Phys. Rev. D 13, 1649 (1976) M. B. Einhorn, ibid. 14, 3451 (1976)
G. 't Hooft, Nucl. Phys. B75, 461 (1974)
J. Bardeen, L. Cooper, and J. Schrieffer, Phys. Rev. 108, 1175 (1957) R. P. Feynman, Statistical Mechanics (Benjamin, New York, 1972)
M. Creutz, Phys. Rev. D 21, 2308 (1980)
J. L. Gervais and A. Neveu, Nucl. Phys. B192, 463 (1982)
G. 't Hooft, Nucl. Phys. B33, 173 (1971) C. Becchi, A. Rouet, and R. Stora, Commun. Math. Phys. 42, 127 (1975) V. S. Dotsenko and S. N. Vergeles, Nucl. Phys. B169, 527 (1980) R. Brandt, F. Neri, and M. Sato, Phys. Rev. D 24, 879 (1981)

[c1] M. Sato, Phys. Lett. 113B, 315 (1982)

[c2] S. Mandelstam, Phys. Rev. D 19, 2391 (1979) R. Giles, 24, 2160 (1981)

[c3] G. 't Hooft, Nucl. Phys. B72, 461 (1974) E. Witten, ibid. B160, 57 (1979) S. Coleman, in The Whys of Subnuclear Physics, proceedings of the International School of Subnuclear Physics, Erice, 1977, edited by A. Zichichi (Plenum, New York, 1979)

[c4] K. Bardakci, Nucl. Phys. B178, 263 (1981) ibid.B193, 245 (1981) M. B. Halpern, ibid. B188, 61 (1981) M. B. Halpern and C. Schwartz, Phys. Rev. D 24, 2146 (1981)

[c5] R. Fukuda, Phys. Lett. 73B, 33 (1978) Phys. Rev. D 21, 485 (1980)

[c6] J. Kogut and L. Susskind, Phys. Rev. D 9, 3501 (1974) G. 't Hooft, in Recent Progress in Lagrangian Field Theory and Applications, proceedings of the Marseilles Colloquium, 1974, edited by C. P. Korthes-Altes (Centre de Physique Theorique, Marseilles, 1975)

[c7] J. Sakamoto and M. Sato, Prog. Theor. Phys. 56, 1617 (1976) R. Utiyama and J. Sakamoto, ibid. 55, 1631 (1976) E. S. Fradkin and I. V. Tyutin, Phys. Rev. D 2, 2841 (1970)

[c8] V. N. Gribov, lecture at the 12th Winter School of the Leningrad Nuclear Physics Institute, 1977 (unpublished)

[c9] T. Kugo and I. Ojima, Suppl. Progr. Theor. Phys. 66, 1 (1979)

[c10] N. N. Bogoliubov, Zh. Eksp. Teor. Fiz. 34, [Sov. Phys. JETP 7, 41 (1958)]

[c11] I. Bars and M. B. Green, Phys. Rev. D 17, 537 (1978)

[c12] C. G. Callan, N. Coote, and D. J. Gross, Phys. Rev. D 13, 1649 (1976) M. B. Einhorn, ibid. 14, 3451 (1976)

[c13] G. 't Hooft, Nucl. Phys. B75, 461 (1974)

[c14] J. Bardeen, L. Cooper, and J. Schrieffer, Phys. Rev. 108, 1175 (1957) R. P. Feynman, Statistical Mechanics (Benjamin, New York, 1972)

[c15] M. Creutz, Phys. Rev. D 21, 2308 (1980)

[c16] J. L. Gervais and A. Neveu, Nucl. Phys. B192, 463 (1982)

[c17] G. 't Hooft, Nucl. Phys. B33, 173 (1971) C. Becchi, A. Rouet, and R. Stora, Commun. Math. Phys. 42, 127 (1975) V. S. Dotsenko and S. N. Vergeles, Nucl. Phys. B169, 527 (1980) R. Brandt, F. Neri, and M. Sato, Phys. Rev. D 24, 879 (1981)

Physical Review D

Export citation

Export citation

Variational methods in the master field formulation for (3+1)-dimensional quantum chromodynamics

Abstract

References (17)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation