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Finite temperature SU(2) lattice gauge theory

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We discuss SU(2) lattice gauge theories at non-zero temperature and prove several rigorous results including i) the absence of confinement for sufficiently high temperature in the pure gauge theory, and ii) the absence of spontaneous chiral symmetry breaking for sufficiently high temperature in the theory with massless fundamental representation fermions.

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References

  1. Tomboulis, E., Yaffe, L.: Nonconfinement at high temperatures. Phys. Rev. D29, 780 (1984); Chiral symmetry restoration at finite temperature. Phys. Rev. Lett.52, 2115 (1984)

    Google Scholar 

  2. Glimm, J., Jaffe, A., Spencer, T.: Phase transitions forφ 42 quantum fields. Commun. Math. Phys.45, 203 (1975)

    Google Scholar 

  3. Fröhlich, J., Lieb, E.: Phase transitions in anisotropic lattice spin systems. Commun. Math. Phys.60, 233 (1978)

    Google Scholar 

  4. See, for example, Simon, B.: TheP(φ)2 Euclidean (quantum) field theory. Princeton, NJ: Princeton University Press 1974

    Google Scholar 

  5. See, for example, Aizenman, M.: Geometric analysis ofφ 4 field and Ising models. Commun. Math. Phys.86, 1–48 (1982); or

    Google Scholar 

  6. Brydges, D., Fröhlich, J., Spencer, T.: The random walk representation of classical spin systems and correlation inequalities. Commun. Math. Phys.83, 123–150 (1982)

    Google Scholar 

  7. See, for example, Ukawa, A., Windey, P., Guth, A.: Dual variables for lattice gauge theories and the phase structure ofZ(N) systems. Phys. Rev. D21, 1013–1036 (1980)

    Google Scholar 

  8. Osterwalder, K., Seiler, E.: Gauge field theories on a lattice. Ann. Phys. (New York)110, 440 (1978)

    Google Scholar 

  9. Brydges, D., Fröhlich, J., Seiler, E.: On the construction of quantized gauge fields. I. General results. Ann. Phys. (New York)121, 227–284 (1979)

    Google Scholar 

  10. Glimm, J., Jaffe, A.: Quantum physics. A functional integral point of view. Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  11. Mack, G., Petkova, V.: Comparison of lattice gauge theories with gauge groupsZ 2 and SU(2). Ann. Phys. (New York)123, 442 (1979)

    Google Scholar 

  12. Yaffe, L.: Confinement in SU(N) lattice gauge theories. Phys. Rev. D21, 1574 (1980)

    Google Scholar 

  13. Borgs, C., Seiler, E.: Lattice Yang-Mills theory of non-zero temperature and the confinement problem. Commun. Math. Phys.91, 329–380 (1983)

    Google Scholar 

  14. Wilson, K.: Confinement of quarks. Phys. Rev. D10, 2445–2459 (1974)

    Google Scholar 

  15. Fröhlich, J., Israel, R., Lieb, E., Simon, B.: Phase transitions and reflection positivity. I. General theory and long range lattice models. Commun. Math. Phys.62, 1–34 (1978)

    Google Scholar 

  16. Fröhlich, J., Israel, R., Lieb, E., Simon, B.: Phase transitions and reflection positivity. II. Lattice systems with short-range and Coulomb interactions. J. Stat. Phys.22, 297–347 (1980)

    Google Scholar 

  17. Polyakov, A.: Thermal properties of gauge fields and quark liberation. Phys. Lett.72B, 477–480 (1978)

    Google Scholar 

  18. McLerran, L., Svetitsky, B.: Quark liberation at high temperature: Monte Carlo study of SU(2) gauge theory. Phys. Rev. D24, 450–460 (1981)

    Google Scholar 

  19. Weiss, N.: Effective potential for the order parameter of gauge theories at finite temperature. Phys. Rev. D24, 475–480 (1981)

    Google Scholar 

  20. See, for example, Fröhlich, J.: Phase transitions, goldstone bosons, and topological superselection rules. Acta. Phys. Austriaca [Suppl.XV] [Schladming 1976] 133–269 (1976); or

    Google Scholar 

  21. Dyson, F., Lieb, E., Simon, B.: Phase transitions in quantum spin systems with isotropic and nonisotropic interactions. J. Stat. Phys.18, 335–383 (1978)

    Google Scholar 

  22. 't Hooft, G.: A property of electric and magnetic flux in non-abelian gauge theories. Nucl. Phys. B153, 141–160 (1979)

    Google Scholar 

  23. See for example, Fontaine, J., Gruber, C.: Surface tension and phase transition for lattice systems. Commun. Math. Phys.70, 243–269 (1979)

    Google Scholar 

  24. Yaffe, L.: See [9]

    Google Scholar 

  25. Susskind, L.: Lattice fermions. Phys. Rev. D16, 3031–3939 (1977)

    Google Scholar 

  26. Sharatchandra, H., Thun, H., Weisz, P.: Susskind fermions on a Euclidean lattice. Nucl. Phys. B192, 205–236 (1981)

    Google Scholar 

  27. Berezin, F.: The method of second quantization. New York: Academic 1966

    Google Scholar 

  28. Glimm, J., Jaffe, A.: Constructive quantum field theory, pp. 199–242. Velo, G., Wightman, A. (eds.). Berlin, Heidelberg, New York: Springer 1973

    Google Scholar 

  29. See, for example, Gross, D.: Methods in field theory, pp. 141–250. Balian, R., Zinn-Justin, J. (eds.). Amsterdam, New York: North-Holland 1976

    Google Scholar 

  30. Seiler, E.: Upper bound on the color-confining potential. Phys. Rev. D18, 482–483 (1978)

    Google Scholar 

  31. 't Hooft, G.: On the phase transition towards permanent quark confinement. Nucl. Phys. B138, 1–25 (1978)

    Google Scholar 

  32. Migdal, A.: Zh. Eksp. Teor. Fiz.69, 810;69, 1457 (1975) [Recursion equations in gauge field theories. Sov. Phys. JETP42, 413–418 (1976); Phase transitions in gauge and spin-lattice systems. Sov. Phys. JETP42, 743–746 (1976)]

    Google Scholar 

  33. Kadanoff, L.: Notes on Migdal's recursion formulas. Ann. Phys. (New York)100, 359–394 (1976)

    Google Scholar 

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Communicated by G. Mack

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Tomboulis, E.T., Yaffe, L.G. Finite temperature SU(2) lattice gauge theory. Commun.Math. Phys. 100, 313–341 (1985). https://doi.org/10.1007/BF01206134

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  • DOI: https://doi.org/10.1007/BF01206134

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