Why is the gauge group for Ashtekar variable theory for General

  1. As far as I understand, the gauge group for Ashtekar variable theory
    for General Relativitiy is SU(2), because its group is three-
    dimensional. But, why is this SU(2) instead of SO(3)? Are there any
    plausible reasonings behind this? And, are there any phenomenological
    differences if the gauge group were SO(3) instead of SU(2)?

    Thanks in advance

    Youngsub
     
  2. jcsd
  3. The Lie group SU(2) is isomorphic to SO(3), that is, they're structurally equivalent.
     
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