Thiemann transform for gravity with matter fields



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Garay Elizondo, Luis Javier and Mena Marugán, Guillermo A. (1998) Thiemann transform for gravity with matter fields. Classical and quantum gravity, 15 (12). pp. 3763-3775. ISSN 0264-9381

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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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© 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.

Uncontrolled Keywords:Quantum-gravity; Fermions; Universe; Origin; State
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:29939
Deposited On:07 May 2015 12:10
Last Modified:10 Dec 2018 15:10

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