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Prog. Theor. Phys. Vol. 70 No. 1 (1983) pp. 229-248

Variational Study of Vacuum Wave Function for Lattice Gauge Theory in 2+1 Dimension

Hiroaki Arisue, Mitsuhiro Kato and Toshiaki Fujiwara^*

Department of Physics, Kyoto University, Kyoto 606
^*Research Institute for Fundamental Physics, Kyoto University, Kyoto 606

(Received March 7, 1983)

Abstract:

The vacuum wave function for SU(2) lattice gauge theory (without quarks) in 2+1 dimensions (two discrete space and one continuous time) is studied using the Rayleigh-Ritz variational method. Trial wave function for the vacuum contains loop variables enclosing up to two plaquettes, whose coefficients we take as variational parameters. It is found that the coefficients of two-plaquette loop variables are small compared with that of one-plaquette loop variables not only in the strong-coupling regime but also in the weak coupling region. This fact means that the dominant configuration of the vacuum is mutually independent magnetic fluctuations in each plaquette and enables us to perform a perturbative expansion with respect to these small coefficients. The string tension and the wave function of the first excited state are investigated using the vacuum wave function obtained, and the scaling behaviours of the string tension and the mass gap are much improved by the introduction of two-plaquette loop variables compared with the case of the vacuum wave function containing only one-plaquette loop variables.

URL : http://ptp.ipap.jp/link?PTP/70/229/
DOI : 10.1143/PTP.70.229

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 84 No. 5 (1990) pp. 951-960 :

   Variational Investigation of the Mass Spectrum in 2+1 Dimensional SU(2) Lattice Gauge Theory

   Hiroaki Arisue

2. Progress of Theoretical Physics Vol. 97 No. 6 (1997) pp. 939-947 :

   Vacuum Wave Functional of Pure Yang-Mills Theory and Dimensional Reduction

   Miyuki Kawamura, Kayoko Maeda and Makoto Sakamoto

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