The Quantum Tetrahedron in 3 and 4 Dimensions
Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use geometric quantization to obtain a Hilbert space of states. Th...
| Main Authors: | , |
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| Format: | Article |
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1999
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| Online Access: | https://eprints.nottingham.ac.uk/10/ |
| _version_ | 1848790342333104128 |
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| author | Baez, John C. Barrett, John W. |
| author_facet | Baez, John C. Barrett, John W. |
| author_sort | Baez, John C. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use geometric quantization to obtain a Hilbert space of states. This Hilbert space has a basis of states labeled by the areas of the faces of the tetrahedron together with one more quantum number, e.g. the area of one of the parallelograms formed by midpoints of the tetrahedron's edges. Repeating the procedure for the tetrahedron in R^4, we obtain a Hilbert space with a basis labelled solely by the areas of the tetrahedron's faces. An analysis of this result yields a geometrical explanation of the otherwise puzzling fact that the quantum tetrahedron has more degrees of freedom in 3 dimensions than in 4 dimensions. |
| first_indexed | 2025-11-14T18:11:05Z |
| format | Article |
| id | nottingham-10 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:11:05Z |
| publishDate | 1999 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-102020-05-04T20:33:05Z https://eprints.nottingham.ac.uk/10/ The Quantum Tetrahedron in 3 and 4 Dimensions Baez, John C. Barrett, John W. Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use geometric quantization to obtain a Hilbert space of states. This Hilbert space has a basis of states labeled by the areas of the faces of the tetrahedron together with one more quantum number, e.g. the area of one of the parallelograms formed by midpoints of the tetrahedron's edges. Repeating the procedure for the tetrahedron in R^4, we obtain a Hilbert space with a basis labelled solely by the areas of the tetrahedron's faces. An analysis of this result yields a geometrical explanation of the otherwise puzzling fact that the quantum tetrahedron has more degrees of freedom in 3 dimensions than in 4 dimensions. 1999 Article PeerReviewed Baez, John C. and Barrett, John W. (1999) The Quantum Tetrahedron in 3 and 4 Dimensions. Adv.Theor.Math.Phys., 3 . pp. 815-850. |
| spellingShingle | Baez, John C. Barrett, John W. The Quantum Tetrahedron in 3 and 4 Dimensions |
| title | The Quantum Tetrahedron in 3 and 4 Dimensions |
| title_full | The Quantum Tetrahedron in 3 and 4 Dimensions |
| title_fullStr | The Quantum Tetrahedron in 3 and 4 Dimensions |
| title_full_unstemmed | The Quantum Tetrahedron in 3 and 4 Dimensions |
| title_short | The Quantum Tetrahedron in 3 and 4 Dimensions |
| title_sort | quantum tetrahedron in 3 and 4 dimensions |
| url | https://eprints.nottingham.ac.uk/10/ |