%0 Journal Article
%A Garay Elizondo, Luis Javier
%A Mena Marugán, Guillermo A.
%T Thiemann transform for gravity with matter fields
%D 1998
%@ 0264-9381
%U https://hdl.handle.net/20.500.14352/59533
%X The generalized Wick transform discovered by Thiemann provides a well established relation between the Euclidean and Lorentzian theories of general relativity. We extend this Thiemann transform to the Ashtekar formulation for gravity coupled with spin-1/2 fermions, a non-Abelian Yang-Mills field and a scalar field. It is proved that, on functions of the gravitational and matter phase space variables, the Thiemann transform is equivalent to the composition of an inverse Wick rotation and a constant complex scale transformation of all fields. This result also holds for functions that depend on the shift vector, the lapse function and the Lagrange multipliers of the Yang-Mills and gravitational Gauss constraints, provided that the Wick rotation is implemented by means of an analytic continuation of the lapse. In this way, the Thiemann transform is furnished with a geometric interpretation. Finally, we confirm the expectation that the generator of the Thiemann transform can be determined just from the spin of the fields and give a simple explanation for this fact.
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