Abstract
I give a very brief review of Ashtekar's variables, with an emphasis on the “non-trivial” reality condition. As a toy model a formulation of spin 1/2 fields is presented, in which the Dirac equation appears as a reality condition. Then, some new ways to modify complex general relativity are mentioned. It is not known whether the new theories admit any reality condition at all.
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Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 211–213, May, 1993.
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Bengtsson, I. Strange reality: Ashtekar's variables with variations. Theor Math Phys 95, 511–513 (1993). https://doi.org/10.1007/BF01017135
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DOI: https://doi.org/10.1007/BF01017135