1998/05/31 by Luis J. Garay, Luis J Garay, Guillermo A. Mena Marugan +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Noncommutative and Quantum Gravity Theories #Quantum and Classical Electrodynamics #gr-qc
paper · pdf · doi:10.1088/0264-9381/15/12/007
published as Class.Quant.Grav. 15 (1998) 3763-3775 · LaTeX 2.09, 14 pages, no figures
openalex publication_date 1998/12/01 · arxiv created 1998/12/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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- 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.