| Abstract: | Ashtekar canonical variables for generalrelativity yielding low degree polynomial constraintsare complex and describe complex canonical gravity. Topick the real sector, a la Dirac, one must introduce reality constraints; they turn out to besecond-class. It is shown here that this holds not onlyfor pure gravity but also for a scalar fieldnon-minimally coupled to gravity. The originalsimplicity produced by the complex variables is spoiled if one getsrid of the second-class constraints via Dirac brackets,however. To circumvent such an undesirable feature,alternative possibilities are pointed out. |
