Abstract
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.
Similar content being viewed by others
References
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)
Glimm, J., Jaffe, A., Spencer, T.: Phase transitions forφ 42 quantum fields. Commun. Math. Phys.45, 203 (1975)
Fröhlich, J., Lieb, E.: Phase transitions in anisotropic lattice spin systems. Commun. Math. Phys.60, 233 (1978)
See, for example, Simon, B.: TheP(φ)2 Euclidean (quantum) field theory. Princeton, NJ: Princeton University Press 1974
See, for example, Aizenman, M.: Geometric analysis ofφ 4 field and Ising models. Commun. Math. Phys.86, 1–48 (1982); or
Brydges, D., Fröhlich, J., Spencer, T.: The random walk representation of classical spin systems and correlation inequalities. Commun. Math. Phys.83, 123–150 (1982)
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)
Osterwalder, K., Seiler, E.: Gauge field theories on a lattice. Ann. Phys. (New York)110, 440 (1978)
Brydges, D., Fröhlich, J., Seiler, E.: On the construction of quantized gauge fields. I. General results. Ann. Phys. (New York)121, 227–284 (1979)
Glimm, J., Jaffe, A.: Quantum physics. A functional integral point of view. Berlin, Heidelberg, New York: Springer 1981
Mack, G., Petkova, V.: Comparison of lattice gauge theories with gauge groupsZ 2 and SU(2). Ann. Phys. (New York)123, 442 (1979)
Yaffe, L.: Confinement in SU(N) lattice gauge theories. Phys. Rev. D21, 1574 (1980)
Borgs, C., Seiler, E.: Lattice Yang-Mills theory of non-zero temperature and the confinement problem. Commun. Math. Phys.91, 329–380 (1983)
Wilson, K.: Confinement of quarks. Phys. Rev. D10, 2445–2459 (1974)
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)
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)
Polyakov, A.: Thermal properties of gauge fields and quark liberation. Phys. Lett.72B, 477–480 (1978)
McLerran, L., Svetitsky, B.: Quark liberation at high temperature: Monte Carlo study of SU(2) gauge theory. Phys. Rev. D24, 450–460 (1981)
Weiss, N.: Effective potential for the order parameter of gauge theories at finite temperature. Phys. Rev. D24, 475–480 (1981)
See, for example, Fröhlich, J.: Phase transitions, goldstone bosons, and topological superselection rules. Acta. Phys. Austriaca [Suppl.XV] [Schladming 1976] 133–269 (1976); or
Dyson, F., Lieb, E., Simon, B.: Phase transitions in quantum spin systems with isotropic and nonisotropic interactions. J. Stat. Phys.18, 335–383 (1978)
't Hooft, G.: A property of electric and magnetic flux in non-abelian gauge theories. Nucl. Phys. B153, 141–160 (1979)
See for example, Fontaine, J., Gruber, C.: Surface tension and phase transition for lattice systems. Commun. Math. Phys.70, 243–269 (1979)
Yaffe, L.: See [9]
Susskind, L.: Lattice fermions. Phys. Rev. D16, 3031–3939 (1977)
Sharatchandra, H., Thun, H., Weisz, P.: Susskind fermions on a Euclidean lattice. Nucl. Phys. B192, 205–236 (1981)
Berezin, F.: The method of second quantization. New York: Academic 1966
Glimm, J., Jaffe, A.: Constructive quantum field theory, pp. 199–242. Velo, G., Wightman, A. (eds.). Berlin, Heidelberg, New York: Springer 1973
See, for example, Gross, D.: Methods in field theory, pp. 141–250. Balian, R., Zinn-Justin, J. (eds.). Amsterdam, New York: North-Holland 1976
Seiler, E.: Upper bound on the color-confining potential. Phys. Rev. D18, 482–483 (1978)
't Hooft, G.: On the phase transition towards permanent quark confinement. Nucl. Phys. B138, 1–25 (1978)
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)]
Kadanoff, L.: Notes on Migdal's recursion formulas. Ann. Phys. (New York)100, 359–394 (1976)
Author information
Authors and Affiliations
Additional information
Communicated by G. Mack
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01206134