Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-10-29
Physics
High Energy Physics
High Energy Physics - Theory
23 pages
Scientific paper
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.
No associations
LandOfFree
Deformation Quantization and Quantum Field Theory on Curved Spaces: the Case of Two-Sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Deformation Quantization and Quantum Field Theory on Curved Spaces: the Case of Two-Sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformation Quantization and Quantum Field Theory on Curved Spaces: the Case of Two-Sphere will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-13452