Quark Condensate in Two-Dimensional SU(NC) Lattice Gauge Theory with Massive Wilson Quarks

  • Using the improved lattice Hamiltonian with massive Wilson quark and the variational method, we study the quark mass mq and the Wilson parameter r dependences of the quark condensate 〈ψψ〉in the two-dimensional SU(NC) lattice gauge theory. The numerical results show that when r is given, for NC=2,3,4,5,6,7, the value of 〈ψψ〉suba/(gNC3/2) decreases as mq increases. For NC>3, when mq is small, 〈ψψ〉suba/(gNC3/2) is almost independent of r; when mq is large, 〈ψψ〉suba/(gNC3/2)increases with increasing r. Particularly, when mq→0, our numerical results agree very well with Zhitnitsky's analytical weak coupling result in the continuum, which implys that our numerical results in the case of mq≠0 are reliable.
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  • [1] . JIANG Jun-Qin, LUO Xiang-Qian et al. Phys. Rev., 1999,D60: 0145012. JIANG Jun-Qin, LUO Xiang-Qian, GUO Shuo-Hong et al.HEP NP, 1999, 23(12): 1152(in Chinese)(江俊勤, 罗向前, 郭硕鸿等. 高能物理与核物理, 1999, 23(12):1152)3. JIANG Jun-Qin, LI Jie-Ming. HEP NP, 2001, 25(7):617(in Chinese)(江俊勤, 李洁明. 高能物理与核物理, 2001, 25(7): 617);JIANG Jun-Qin. HEP NP, 2005, 29(2): 115(in Chinese)(江俊勤. 高能物理与核物理, 2005, 29(2):115)4. JIANG Jun-Qin, LI Jie-Ming. Phys. Rev., 2003, D68:0945025. 't Hooft G. Nucl. Phys., 1974, B72: 4616. Steinhardt P J. Nucl. Phys., 1980, B176: 1007. Bhattacharya G. Nucl. Phys., 1982, B205: 4618. Zhitnitsky A R. Phys. Lett., 1985, B165: 4059. LUO Xiang-Qian, CHEN Qi-Zhou. HEP NP, 1992,16(8): 676(in Chinese)(罗向前, 陈启洲. 高能物理与核物理, 1992, 16(8): 676)
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JIANG Jun-Qin. Quark Condensate in Two-Dimensional SU(NC) Lattice Gauge Theory with Massive Wilson Quarks[J]. Chinese Physics C, 2007, 31(1): 19-22.
JIANG Jun-Qin. Quark Condensate in Two-Dimensional SU(NC) Lattice Gauge Theory with Massive Wilson Quarks[J]. Chinese Physics C, 2007, 31(1): 19-22. shu
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Received: 2006-03-24
Revised: 2006-07-02
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Quark Condensate in Two-Dimensional SU(NC) Lattice Gauge Theory with Massive Wilson Quarks

    Corresponding author: JIANG Jun-Qin,
  • Department of Physics,Guangdong Institute of Education, Guangzhou 510303, China

Abstract: Using the improved lattice Hamiltonian with massive Wilson quark and the variational method, we study the quark mass mq and the Wilson parameter r dependences of the quark condensate 〈ψψ〉in the two-dimensional SU(NC) lattice gauge theory. The numerical results show that when r is given, for NC=2,3,4,5,6,7, the value of 〈ψψ〉suba/(gNC3/2) decreases as mq increases. For NC>3, when mq is small, 〈ψψ〉suba/(gNC3/2) is almost independent of r; when mq is large, 〈ψψ〉suba/(gNC3/2)increases with increasing r. Particularly, when mq→0, our numerical results agree very well with Zhitnitsky's analytical weak coupling result in the continuum, which implys that our numerical results in the case of mq≠0 are reliable.

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