Advertisement

Lattice Gauge Theories

  • Michael Creutz
Part of the Progress in Physics book series (PMP, volume 8)

Abstract

In the last few years lattice gauge theory has become the primary tool for the study of nonperturbative phenomena in gauge theories. The lattice serves as an ultraviolet cutoff, rendering the theory well defined and amenable to numerical and analytical work. Of course, as with any cutoff, at the end of a calculation one must consider the limit of vanishing lattice spacing in order to draw conclusions on the physical continuum limit theory. The lattice has the advantage over other regulators that it is not tied to the Feynman expansion. This opens the possibility of other approximation schemes than conventional perturbation theory. Thus Wilson used a high temperature expansion to demonstrate confinement in the strong coupling limit. Monte Carlo simulations have dominated the research in lattice gauge theory for the last four years, giving first principle calculations of nonperturbative parameters characterizing the continuum limit.

Keywords

Gauge Theory Continuum Limit Gauge Field Lattice Gauge Theory Strong Coupling Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    S. Coleman and E. Weinberg, Phys. Rev. D7 (1973) 1888.Google Scholar
  2. [2]
    D. Gross and F. Wilczek, Phys. Rev. Lett. 30 (1973) 1343; Phys. Rev. D8 (1973) 3633; W.E. Caswell, Phys. Rev. Lett. 33 (1974)244; D.R.T. Jones, Nucl. Phys. B75 (1974) 531.CrossRefGoogle Scholar
  3. [3]
    M. Creutz and K.J.M. Moriarty, Phys. Rev. D26 (1982) 2166.Google Scholar
  4. [4]
    A. Hasenfratz and P. Hasenfratz, Phys. Lett. 93B (1980) 165.Google Scholar
  5. [5]
    K. Wilson, Phys. Rev. D10 (1974) 2445.Google Scholar
  6. [6]
    R. Balian, J.M. Drouffe, C. Itzykson, Phys. Rev. D10 (1974) 3376; D11 (1975) 2098; D11 (1975) 2104.Google Scholar
  7. [7]
    L.P. Kadanoff, Rev. Mod. Phys. 49 (1977) 267.CrossRefGoogle Scholar
  8. [8]
    K.M. Bitar, S. Gottlieb, C. Zachos, Phys. Rev. D26 (1982) 2853.CrossRefGoogle Scholar
  9. [19]
    E. Tomboulis, Phys. Rev Lett. 50 (1983) 885.CrossRefGoogle Scholar
  10. [10]
    H. Creutz, L. Jacobs, C. Rebbi, Physics Reports (In press).Google Scholar
  11. [11]
    L. McClerran and B. Svetitsky, Phys. Lett. 98B (1981)195; J. J. Kuti, J. Polonyi, K. Szlachanyi, Phys. Lett. 98B (1981) 199; K. Kajantie, C. Montonen, E. Pietarinen, Zeit. Phys. C9 (1981) 253; J. Engels, F. Karsch, H. Satz, J. Montvay, Phys. Lett. 101B (1981) 89; Nucl. Phys. B205 (1982) 545.Google Scholar
  12. [12]
    K. Johnson, talk at this conference.Google Scholar
  13. [13]
    B. Berg and A. Billoire, Phys. Lett. 114B (1982)324; K. Ishlkava, C. Schlerholz, M. Teper, Phys. Lett. 110B (1982) 399.Google Scholar
  14. [14]
    D. Weingarten and D. Petcher, Phys. Lett. 99B (1981) 333.Google Scholar
  15. [15]
    F. Fucito, E. Marinari, G. Parisi, C. Rebbi, Nucl. Phys. B180 (1981) 369.CrossRefGoogle Scholar
  16. [16]
    H. Hamber, E. Marinari, C. Parisi, C. Rebbi, preprint (1983).Google Scholar
  17. [17]
    J. Kutl, Phys. Rev. Lett. 49 (1982) 183.CrossRefGoogle Scholar
  18. [18]
    W. Duffy, G. Guralnik, D. Weingarten, preprint (1983)Google Scholar
  19. [19]
    D. Welngarten, Phys. Lett. 109B (1982)57; H. Hamber and G. Parisi, Phys. Rev. Lett. 47 (1982) 1792; E. Marinari, G. Parisi, C. Rebbi, Phys. Rev. Lett. 47 (1981) 1798.Google Scholar
  20. [20]
    D. Callaway and A. Rahman, Phys. Rev. Lett. 49 (1982) 613.CrossRefGoogle Scholar
  21. [21]
    M. Creutz, preprint (1983).Google Scholar

Copyright information

© Birkhäuser Boston, Inc. 1983

Authors and Affiliations

  • Michael Creutz
    • 1
  1. 1.Physics DepartmentBrookhaven National LaboratoryUptonUSA

Personalised recommendations