Hamiltonian formulation of Palumbo's noncompact lattice gauge theory

B. Diekmann; D. Schütte; H. Kröger

doi:10.1103/PhysRevD.49.3589

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Hamiltonian formulation of Palumbo's noncompact lattice gauge theory

B. Diekmann and D. Schütte

H. Kröger

Institut für Theoretische Kernphysik, Universität Bonn, Nussallee 14-16, D-53115 Bonn, Germany

Max Planck Institut für Kernphysik, P.O.B. 10 39 80, D-69029 Heidelberg, Germany
Département de Physique, Université Laval, Québec, Québec G1K 7P4, Canada

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Phys. Rev. D 49, 3589 – Published 1 April, 1994

DOI: https://doi.org/10.1103/PhysRevD.49.3589

Abstract

We analyze Palumbo's noncompact, manifestly gauge-invariant, lattice gauge theory. Via the transfer matrix we construct from Palumbo's action the corresponding Hamiltonian. In the classical continuum limit we recover the Kogut-Susskind Hamiltonian. We also study the confinement structure of the theory by computing the Wilson loop in the strong coupling regime. We find an area-law behavior for both U(1) and SU(2) gauge theory in that regime.

References (12)

K.G. Wilson, Phys. Rev. D 10, 2445 (1974)
J. Kogut and L. Susskind, Phys. Rev. D 11, 395 (1975)
D. Horn et al., Phys. Rev. D 31, 2589 (1985) S.A. Chin et al., ibid. 37, 3001 (1988) M.K. Mak and D. Schütte, "A cluster expansion in lattice gauge theories" (unpublished)
R.E. Cutkosky et al., Phys. Rev D 42, 1260 (1990) S. Nojiri, Z. Phys. C 22, 245 (1984) B. Rosenstein et al., Phys. Lett. B 177, 71 (1986) D. Schütte et al., Phys. Rev. D 34, 1157 (1986) ibid.40, 2692 (1989) ibid.43, 1991 (1991) Ann. Phys. (N.Y.) 211, 112 (1991)
A. Patrascioiu, E. Seiler, and I. Stamatescu, Phys. Lett. 107B, 364 (1981) I. Stamatescu, U. Wolff, and D. Zwanziger, Nucl. Phys. B225, 377 (1983) E. Seiler, I. Stamatescu, and D. Zwanziger, ibid. B239, 177 (1984) ibid.B239, 201 (1984) K. Cahill, in Lattice '90, Proceedings of the International Symposium, Tallahassee, Florida, 1990, edited by U.M. Heller [Nucl. Phys. B (Proc. Suppl.) 20, 240 (1991)]
F. Palumbo, Phys. Lett. B 244, 55 (1990) ibid.250, 212 (1990) F. Palumbo, M.I. Polikarpov, and A.I. Veselov, ibid. 258, 189 (1991) C.M. Becchi and F. Palumbo, Phys. Rev. D 44, R946 (1991) Nucl. Phys. B388, 595 (1992)
F. Palumbo, M.I. Polikarpov, and A.I. Veselov, Phys. Lett. B 297, 171 (1992)
M. Lüscher, Nucl. Phys. B219, 233 (1983) J. Koller and P. van Baal, ibid. B302, 1 (1988)
B. Borasoy, B. Diekmann, W. Kramer, and D. Schütte (unpublished)
M. Creutz, Phys. Rev. D 15, 1128 (1977)
N.H. Christ and T.D. Lee, Phys. Rev. D 22, 939 (1980)
M. Creutz, Quarks, Gluons and Lattices (Cambridge University Press, Cambridge, England, 1983)

[c1] K.G. Wilson, Phys. Rev. D 10, 2445 (1974)

[c2] J. Kogut and L. Susskind, Phys. Rev. D 11, 395 (1975)

[c3] D. Horn et al., Phys. Rev. D 31, 2589 (1985) S.A. Chin et al., ibid. 37, 3001 (1988) M.K. Mak and D. Schütte, "A cluster expansion in lattice gauge theories" (unpublished)

[c4] R.E. Cutkosky et al., Phys. Rev D 42, 1260 (1990) S. Nojiri, Z. Phys. C 22, 245 (1984) B. Rosenstein et al., Phys. Lett. B 177, 71 (1986) D. Schütte et al., Phys. Rev. D 34, 1157 (1986) ibid.40, 2692 (1989) ibid.43, 1991 (1991) Ann. Phys. (N.Y.) 211, 112 (1991)

[c5] A. Patrascioiu, E. Seiler, and I. Stamatescu, Phys. Lett. 107B, 364 (1981) I. Stamatescu, U. Wolff, and D. Zwanziger, Nucl. Phys. B225, 377 (1983) E. Seiler, I. Stamatescu, and D. Zwanziger, ibid. B239, 177 (1984) ibid.B239, 201 (1984) K. Cahill, in Lattice '90, Proceedings of the International Symposium, Tallahassee, Florida, 1990, edited by U.M. Heller [Nucl. Phys. B (Proc. Suppl.) 20, 240 (1991)]

[c6] F. Palumbo, Phys. Lett. B 244, 55 (1990) ibid.250, 212 (1990) F. Palumbo, M.I. Polikarpov, and A.I. Veselov, ibid. 258, 189 (1991) C.M. Becchi and F. Palumbo, Phys. Rev. D 44, R946 (1991) Nucl. Phys. B388, 595 (1992)

[c7] F. Palumbo, M.I. Polikarpov, and A.I. Veselov, Phys. Lett. B 297, 171 (1992)

[c8] M. Lüscher, Nucl. Phys. B219, 233 (1983) J. Koller and P. van Baal, ibid. B302, 1 (1988)

[c9] B. Borasoy, B. Diekmann, W. Kramer, and D. Schütte (unpublished)

[c10] M. Creutz, Phys. Rev. D 15, 1128 (1977)

[c11] N.H. Christ and T.D. Lee, Phys. Rev. D 22, 939 (1980)

[c12] M. Creutz, Quarks, Gluons and Lattices (Cambridge University Press, Cambridge, England, 1983)

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Hamiltonian formulation of Palumbo's noncompact lattice gauge theory

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References (12)

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