Intermediate Volumes and the Role of Instantons

  • Pierre van Baal
Conference paper
Part of the Centre de Physique des Houches book series (LHWINTER, volume 8)

Abstract

An outstanding problem is to understand the formation of a mass gap and the spectrum of excitations in a non-Abelian gauge theory. Non-perturbative aspects are believed to play a crucial role, but despite much progress a simple explanation is still lacking. Over the years we have been interested in addressing this problem in a finite volume, where its size can be used as a control parameter, which is conspicuously absent in infinite volumes, in particular for formulating the binding of gluons in glueballs. Much progress was made in intermediate volumes with a torodial geometry, where results can be directly compared to lattice Monte Carlo calculations in the same physical volume [1].

Keywords

Manifold 

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References

  1. [1]
    van Baal P., Phys.Lett. 224B (1989) 397;ADSGoogle Scholar
  2. [1a]
    van Baal P., Nucl. Phys. B351 (1991) 183.ADSCrossRefGoogle Scholar
  3. [2]
    Löscher M., Nucl.Phys. B219 (1983) 233ADSCrossRefGoogle Scholar
  4. [3]
    van Baal P. and Hari Dass N.D., Nucl.Phys. B385 (1992) 185.ADSCrossRefGoogle Scholar
  5. [4]
    Babelon O. and Viallet C., Comm.Math.Phys. 81 (1981) 515.MathSciNetADSMATHCrossRefGoogle Scholar
  6. [5]
    Singer I., Comm.Math.Phys. 60 (1978) 7.MathSciNetADSMATHCrossRefGoogle Scholar
  7. [6]
    Gribov V., Nucl.Phys. B139(1978) 1.MathSciNetADSCrossRefGoogle Scholar
  8. [7]
    Nahm W., in: IV Warsaw Sym.Elem.Part.Phys, 1981, ed. Z.Ajduk, p.275.Google Scholar
  9. [8]
    van Baal P., in: Probabilistic Methods in Quantum Field Theory and Quantum Gravity, Damgaard P.H. et al, ed. (Plenum Press, New York, 1990) p31;Google Scholar
  10. [8]
    van Baal P., Nucl.Phys. B(Proc.Suppl.)20 (1991) 3.MATHCrossRefGoogle Scholar
  11. [9]
    Semenov-Tyan-Shanskii M.A. and Franke V.A., Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V.A. Steklov AN SSSR, 120 (1982) 159. Translation: (Plenum Press, New York, 1986) p.999;MathSciNetGoogle Scholar
  12. [9a]
    Zwanziger D., Nucl. Phys. B209 (1982) 336.Google Scholar
  13. [10]
    Christ N.M. and Lee T.D., Phys.Rev. D22 (1980) 939.MathSciNetADSGoogle Scholar
  14. [11]
    Dell’Antonio G. and Zwanziger D., Nucl.Phys. B326 (1989) 333.MathSciNetADSCrossRefGoogle Scholar
  15. [12]
    van Baal P., Nucl.Phys. B369 (1992) 259.ADSCrossRefGoogle Scholar
  16. [13]
    van Baal P. and van den Heuvel B., Nucl.Phys. B417 (1994) 215.ADSCrossRefGoogle Scholar
  17. [14]
    ’t Hooft G., Phys.Rev. D14 (1976) 3432.ADSGoogle Scholar
  18. [15]
    van den Heuvel B.M, Phys.Lett. B368 (1996) 124;ADSGoogle Scholar
  19. [15a]
    van den Heuvel B.M, Phys.Lett. B386 (1996) 233;ADSGoogle Scholar
  20. [b]
    van den Heuvel B.M, Nucl.Phys. B488 (1997) 282.ADSCrossRefGoogle Scholar
  21. [16]
    Michael C. and Teper M., Phys.Lett. B199 (1987) 95.ADSGoogle Scholar
  22. [17]
    van Baal P., Global issues in gauge fixing, in: “Non-perturbative approaches to Quantum Chromodynamics”, ed. D. Diakonov, (Gatchina, 1995) p.4.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Pierre van Baal
    • 1
    • 2
  1. 1.Isaac Newton Institute for Mathematical SciencesCambridgeUK
  2. 2.Instituut-Lorentz for Theoretical PhysicsUniversity of LeidenRA LeidenThe Netherlands

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