  Using a key observation due to Thiemann, a generalized Wick transform is
introduced to map the constraint functionals of Riemannian general relativity
to those of the Lorentzian theory, including matter sources. This opens up a
new avenue within ``connection-dynamics'' where one can work, throughout, only
with real variables. The resulting quantum theory would then be free of
complicated reality conditions. Ramifications of this development to the
canonical quantization program are discussed.
