RT Journal Article
T1 Thiemann transform for gravity with matter fields
A1 Garay Elizondo, Luis Javier
A1 Mena Marugán, Guillermo A.
AB 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.
PB IOP Publishing Ltd
SN 0264-9381
YR 1998
FD 1998-12
LK https://hdl.handle.net/20.500.14352/59533
UL https://hdl.handle.net/20.500.14352/59533
LA eng
NO © IOP Publishing. The authors are grateful to P. F. González Díaz for helpful conversations. This work was supported by funds provided by the DGICYT Project No. PB94–0107.
NO DGICYT
DS Docta Complutense
RD 17 abr 2025