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Vacuum energy for Yang-Mills fields inR d ×S1: One-loop, two-loop, and beyond

  • K. Shiraishi
  • S. Hirenzaki
Article

Abstract

The vacuum energy is calculated for Yang-Mills (YM) system defined inD dimensional space-time ofS1×R d (D=d+1), where the possibility of the YM fields to acquire the vacuum expectation values onS1 is taken into account. The vacuum energy has already been obtained to the order of one-loop in many people. Here we calculate the vacuum energy inD dimensions to two-loop order. With an intention to reach higher loops, an approximation method is proposed, which is especially effective in higher dimensions. By this method, we can treat the higher-loop contributions of YM interactions as easily as we treat one-loop effect. As a check, we show reproduction of the two-loop contribution (D-dependence of the coefficient as well as the functional form) when the coupling constant is small. This approximation method is useful not only for the Kaluza-Klein theories but also for the finite temperature-density system (as a quark-gluon plasma).

Keywords

Elementary Particle Quantum Field Theory Approximation Method Functional Form High Dimension 
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References

  1. 1.
    G. Plunien, B. Müller, W. Greiner: Phys. Rep.134 (1986) 87; V.M. Mostepanenko, N.N. Trunov: Sov. Phys. Usp. 31 (1988) 965Google Scholar
  2. 2.
    G. Barton, N.S.J. Fawcett: Phys. Rep. 170 (1988) 1Google Scholar
  3. 3.
    B.S. De Witt: Phys. Rep. 19 (1975) 295; L.H. Ford: Phys. Rev. D11 (1975) 3370; D14 (1976) 3304; D.J. Toms: Phys. Rev. D21 (1980) 928; 2805Google Scholar
  4. 4.
    D. Bailin, A. Love: Rep. Prog. Phys. 50 (1987) 1087; V.M. Emel'yanov et al.: Phys. Rep. 143 (1986) 1; I. Ya. Aref'eva, I.V. Volovich: Sov. Phys. Usp. 28 (1985) 694Google Scholar
  5. 5.
    T. Appelquist, A. Chodos: Phys. Rev. D28 (1983) 772; T. Inami, O. Yasuda: Phys. Lett. B133 (1983) 180; P. Candelas, S. Weinberg: Nucl. Phys. B237 (1984) 397Google Scholar
  6. 6.
    M.B. Green, J.H. Schwarz, E. Witten: Superstring theory, 2 volumes. Cambridge: Cambridge Univ. Press 1987Google Scholar
  7. 7.
    Y. Hosotani: Phys. Lett. B126 (1983) 445; for more references on Hosotani mechanism, see: K. Shiraishi: Can. J. Phys. 68 (1990) 357Google Scholar
  8. 8.
    Y. Kato, J. Saito: Prog. Theor. Phys. 74 (1985) 1145; O. Foda: preprint IC/84/238 (December 1984), unpublished; E.J. Copeland, D.J. Toms: Nucl. Phys. B255 (1985) 201; I.H. Russell, D.J. Toms: Class. Quantum Grav. 4 (1987) 1357Google Scholar
  9. 9.
    R.B. Mann et al.: Nucl. Phys. B311 (1988/89) 630Google Scholar
  10. 10.
    J.I. Kapusta: Nucl. Phys. B148 (1979) 461; K. Kajantie, J.I. Kapusta: Ann. Phys. (NY) 160 (1985) 477; see also: J.I. Kapusta, P.V. Landshoff: J. Phys. G15 (1989) 267, for further referencesGoogle Scholar
  11. 11.
    V.M. Belyaev, V.L. Eletskii: JETP Lett. 50 (1989) 55; V.M. Belyaev, V.L. Eletskii: Sov. J. Nucl. Phys. 51 (1990) 168; V.M. Belyaev, V.L. Eletsky: Z. Phys. C—Particles and Fields 45 (1990) 355; V.M. Belyaev: Phys. Lett. B241 (1990) 91; K. Enqvist, K. Kajantie: Z. Phys. C—Particles and Fields 47 (1990) 291Google Scholar
  12. 12.
    H.-Th. Elze, U. Heinz, K. Kajantie, T. Toimela: Z. Phys. C—Particles and Fields 37 (1988) 305Google Scholar
  13. 13.
    A. Nakamura, K. Shiraishi: preprint OCHA-PP-11 (1990)Google Scholar
  14. 14.
    B.A. Campbell et al.: Phys. Lett. B197 (1987) 355Google Scholar
  15. 15.
    S. Coleman, R. Jackiw, H.D. Politzer: Phys. Rev. D10 (1974) 2491Google Scholar
  16. 16.
    K. Enqvist, K. Kajantie: Z. Phys. C—Particles and Fields 47 (1990) 291Google Scholar
  17. 17.
    K. Redlich, L. Turko: Z. Phys. C—Particles and Fields 5 (1980) 201; L. Turko: Phys. Lett. B104 (1981) 153; M.I. Gorenstein et al.: Z. Phys. C—Particles and Fields 18 (1983) 13; M.I. Gorenstein et al.: Phys. Lett. B123 (1983) 437; B. Müller, J. Rafelski: Phys. Lett. B116 (1982) 274; H.-Th. Elze, W. Greiner, J. Rafelski: Phys. Lett. B124 (1983) 515; H.-Th. Elze, W. Greiner, J. Rafelski: Z. Phys. C—Particles and Fields 24 (1984) 361; H.-Th. Elze, W. Greiner: Phys. Lett. B179 (1986) 385; See also: B. Müller: The Physics of the Quark-Gluon Plasma. Lecture Notes in Physics 225, Berlin, Heidelberg, New York: Springer 1985Google Scholar
  18. 18.
    V.M. Belyaev: Phys. Lett. B254 (1991) 153Google Scholar
  19. 19.
    K. Shiraishi, S. Hirenzaki: in preparationGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • K. Shiraishi
    • 1
  • S. Hirenzaki
    • 2
  1. 1.Department of Physics, Faculty of ScienceOchanomizu UniversityTokyoJapan
  2. 2.Department of PhysicsTokyo Metropolitan UniversityTokyoJapan

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