中国物理B ›› 2002, Vol. 11 ›› Issue (4): 327-331.doi: 10.1088/1009-1963/11/4/304

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On the problem of reality conditions for the Ashtekar formulation

吴亚波1, 李磊1, 李久利2   

  1. (1)Department of Physics, Liaoning Normal University, Dalian 116029, China; (2)National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
  • 收稿日期:2001-10-03 修回日期:2001-12-01 出版日期:2002-04-13 发布日期:2005-06-13
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 19833020).

On the problem of reality conditions for the Ashtekar formulation

 Li Jiu-Li (李久利)a, Wu Ya-Bo (吴亚波)b, Li Lei (李磊)b   

  1. a  National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China; b  Department of Physics, Liaoning Normal University, Dalian 116029, China
  • Received:2001-10-03 Revised:2001-12-01 Online:2002-04-13 Published:2005-06-13
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 19833020).

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摘要： In this paper we discuss the reality conditions for Lorentzian and Euclidean gravity in the Ashtekar formulation by introducing a double conformal transformation. We generalize Marugan's results and demonstrate that the values of the double conformal factor have to be either real or double complex numbers. Either Lorentzian or Euclidean gravitational theory is up to the different values of the double conformal factor. Furthermore, the reality conditions of Lorentzian and Euclidean gravitational theory can be expressed in a unified way by use of the double complex function method.

Abstract: In this paper we discuss the reality conditions for Lorentzian and Euclidean gravity in the Ashtekar formulation by introducing a double conformal transformation. We generalize Marugan's results and demonstrate that the values of the double conformal factor have to be either real or double complex numbers. Either Lorentzian or Euclidean gravitational theory is up to the different values of the double conformal factor. Furthermore, the reality conditions of Lorentzian and Euclidean gravitational theory can be expressed in a unified way by use of the double complex function method.

Key words: Ashtekar formulation, reality conditions, conformal transformation

中图分类号:  (Exact solutions)

  • 04.20.Jb
04.60.-m (Quantum gravity)