Deformation Quantization and Quantum Field Theory on Curved Spaces: the Case of Two-Sphere
| dc.creator | Zhou, Chengang | |
| dc.date | 2001-10-29 | |
| dc.date.accessioned | 2026-07-07T04:12:35Z | |
| dc.date.available | 2026-07-07T04:12:35Z | |
| dc.description | We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized by $H^2(S^2, \QR)$. The fuzzy sphere is included as a special case parametrized by the integer two-cohomology class $H^2(S^2, \QZ)$, which has finite number of degrees of freedom and the field theory has a well defined Hilbert space. When the two-cohomology class is not integer valued, the scalar quantum field theory based on the deformation algebra is not unitary: the signature of the inner product on the space of functions is indefinite. Hence the existence of deformation quantization does not guarantee a physically acceptable deformed geometric background. For the deformation quantization on a general curved space, this obstruction of unitarity can be given by an explicit topological formula. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/0110268 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0110268 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/50952 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Deformation Quantization and Quantum Field Theory on Curved Spaces: the Case of Two-Sphere | |
| dc.type | text |