Abstract
The ideal,SU(N c ) coloured, quark-gluon gas partition function is considered, taking the global colour-singlet condition into account. The coloursinglet condition leads to finite volume corrections to the thermodynamical quantities of the gas. Possible effects of these finite volume corrections on lattice QCD at a finite temperature are discussed. Recent Monte Carlo evaluations of the energy density inSU(2) andSU(3) Yang-Mills lattice gauge theories are consistent with such corrections. In the largeN c -limit, a phase transition is exhibited which, formally, has the same origin as a largeN c -limit phase transition in the two-dimensionalSU(N c ) lattice gauge theory.
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H.A. Bethe: Phys. Rev.50, 331 (1936); E. Fermi: Prog. Theor. Phys. (Japan)1, 510 (1950); Z. Koba: Nuovo Cimento18, 608 (1961); T. Ericson: Nuovo Cimento21, 605 (1961); F. Cerulus: Nuovo Cimento22, 958 (1961); H. Satz: Fortschr. Phys.11, 445 (1963); H. Joos, H. Satz; Nuovo Cimento34, 619 (1964); K.Z. Zalewski: Acta Phys. Polon.28, 207 (1965); J.S. Bell, G. Karl, C.L. Llewellyn Smith: Phys. Lett.52, 363 (1974); J. van der Meulen, in: Proc. Symp. on Nucleon-antinucleon annihilations, ed. L. Montanet (Chexbres, 1972) CERN 72-10, 1972; B. Müller, J. Rafelski: Phys. Lett.116B, 274 (1982)
D. Horn, R. Silver: Ann. Phys. (N.Y.)66, 509 (1971); D. Horn, F. Zachariasen: Hadron physics at very high energies, New York: Benjamin, 1973; J.C. Botke, D.J. Scalapino, R.L. Sugar: Phys. Rev.D9, 813 (1974)
B.A. Freedman, L.D. McLerran, Phys. Rev.D16, 1169 (1977); S.A. Chin: Phys. Lett.78B, 552 (1978); B.A. Freedman, L.D. McLerran: Phys. Rev.D16, 1169 (1977); S.A. Chin: Phys. Lett.78B, 552 (1978); P.D. Morley, M.B. Kislinger: Phys. Rep.51, 63 (1979); J.I. Kapusta: Nucl. Phys.B148, 461 (1979); O.K. Kalashnikov, V.V. Kilmov: Phys. Lett.88B, 328 (1979); E.V. Shuryak: Phys. Lett.81B, 65 (1979); Phys. Rep.61, 71 (1980); R. Anishetty, P. Koehler, L. McLerran: Phys. Rev.D22, 2793 (1980); J. Rafelski, R. Hagedorn, in: Thermodynamics of quarks and hadrons. ed. H. Satz Amsterdam: North-Holland (1981); and in: Proc. of 5th European Symposium on Nucleon-antinucleon interactions, Padova, 1980; G. Domokos, J.I. Goldman: Phys. Rev.D23, 203 (1981); K. Kajantie, H.I. Mietinnen: Z. Phys. C—Particles and Fields9, 341 (1981); ibid.14, 357 (1982)
L. Turko: Phys. Lett.104B, 153 (1981); K. Redlich, L. Turko: Z. Phys. C—Particles and Fields5, 201 (1980)
H.-Th. Elze, W. Greiner, J. Rafelski: Phys. Lett.124B, 515 (1983)
M.I. Gorenstein, O.A. Mogilevsky, V.K. Petrov G.M. Zinovjev: Z. Phys. C—Particles and Fields 13 (1983); M.I. Gorenstein, S.I. Lipskikh, V.K. Petrov and G.M. Zinovjev: Phys. Lett.123B, 437 (1983)
K.-E. Eriksson, N. Mukunda, B.-S. Skagerstam: Phys. Rev.D24, 2615 (1981)
B.-S. Skagerstam: Quasicoherent states for unitary groups, Göteborg preprint (83-38) 1983, to be published.
D.J. Gross, E. Witten: Phys. Rev.D21, 446 (1980)
J. Engels, F. Karsch, I. Montvay, H. Satz: Nucl. Phys.B205 [FS5], 545 (1982); T. Celik, J. Engels, H. Satz: Phys. Lett.129B, 419 (1983)
J.R. Klauder, E.C.G. Sudarshan: Fundamentals of quantum optics. New York Benjamin 1968
H. Weyl: The classical groups. Princeton: Princeton University Press 1946
S. Wadia: University of Chicago preprint EFI 79/44 (1979) unpublished; C.B. Lang, P. Salomonson, B.-S. Skagerstam: Nucl. Phys.B190, [FS3] 337 (1981)
J.R. Klauder: Acta Phys. Austr. suppl.18, 1 1977
Y. Ohnuki: lectures given at National Laboratory for High Energy Physics (KEK), Tsukuba (1977)
F.A. Berezin: The method of second quantization. New York: Academic Press, 1966
B.-S. Skagerstam: Phys. Rev.D19, 2471 (1979); ibid. Phys. Rev.D22, 534(E) (1980)
T. Chen, C.I. Tan, X. Zheng: Phys. Lett.109B, 383 (1982); Yu. M. Makeenko, M.I. Polikatpov: Nucl. Phys.B205, [FS5] 386 (1982); S. Samuel: Phys. Lett.112B, 237 (1982); M.C. Ogilvie, A. Horowitz: Nucl. Phys.B215, [FS7], 249 (1983)
J. Rafelski, M. Danos: to appear.
C. Borgs, E. Seiler: Nucl. Phys.B215, [FS7], 125 (1983); Commun. Math. Phys.91, 329 (1983)
B.-S. Skagerstam: Phys. Lett.133B, 419 (1983)
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On leave of absence from the Institute of Theoretical Physics,
On leave of absence from the Institute of Theoretical Physics,
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Skagerstam, B.S. On the largeN c limit of theSU(N c ) colour quark-gluon partition function. Z. Phys. C - Particles and Fields 24, 97–101 (1984). https://doi.org/10.1007/BF01576294
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DOI: https://doi.org/10.1007/BF01576294