Thiemann transform for gravity with matter fields
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...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1998 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/59533 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/59533 |
| Access Level: | acceso abierto |
| Palabra clave: | 51-73 Quantum-gravity Fermions Universe Origin State Física-Modelos matemáticos Física matemática |
| Sumario: | 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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