Why is the gauge group for Ashtekar variable theory for General

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SUMMARY

The gauge group for Ashtekar variable theory in General Relativity is definitively SU(2), which is a three-dimensional group. This choice is based on the structural equivalence between SU(2) and SO(3), as they are isomorphic. However, the implications of using SO(3) instead of SU(2) in this context raise questions about potential phenomenological differences, warranting further exploration.

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  • Understanding of gauge theory in physics
  • Familiarity with Lie groups, specifically SU(2) and SO(3)
  • Knowledge of General Relativity principles
  • Basic concepts of isomorphism in mathematics
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Physicists, mathematicians, and students interested in gauge theories, particularly those studying General Relativity and its mathematical foundations.

yyoon@fas.harvard.edu
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
 
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The Lie group SU(2) is isomorphic to SO(3), that is, they're structurally equivalent.
 

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