| Автор | R J Henderson |
| Автор | S G Rajeev |
| Дата выпуска | 1994-07-01 |
| dc.description | We study a model for quantum gravity on a circle in which the notion of a classical metric tensor is replaced by a quantum metric with an inhomogeneous transformation law under diffeomorphisms. This transformation law corresponds to the co-adjoint action of the Virasoro algebra, and resembles that of the connection in Yang--Mills theory. The transformation property is motivated by the diffeomorphism invariance of the one-dimensional Schrödinger equation. The quantum distance measured by the metric corresponds to the phase of a quantum mechanical wavefunction. The dynamics of the quantum gravity theory are specified by postulating a Riemann metric on the space, Q, of quantum metrics and taking the kinetic energy operator to be the resulting Laplacian on the configuration space . The resulting metric on the configuration space is analysed and found to have singularities. The second-quantized Schrödinger equation is derived, some exact solutions are found, and a generic wavefunction behaviour near one of the metric singularities is described. Finally, some directions for further study are indicated, including an analogue of the Yamabe problem of differential geometry. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Quantum gravity on a circle and the diffeomorphism invariance of the Schrödinger equation |
| Тип | paper |
| DOI | 10.1088/0264-9381/11/7/006 |
| Electronic ISSN | 1361-6382 |
| Print ISSN | 0264-9381 |
| Журнал | Classical and Quantum Gravity |
| Том | 11 |
| Первая страница | 1631 |
| Последняя страница | 1651 |
| Аффилиация | R J Henderson; Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA |
| Аффилиация | S G Rajeev; Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA |
| Выпуск | 7 |
