Field theory on the q-deformed fuzzy sphere II: quantization

✍ Scribed by H. Grosse; J. Madore; H. Steinacker

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 292 KB
• Volume: 43
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00023-2

✦ Synopsis

We study the second quantization of field theory on the q-deformed fuzzy sphere for q ∈ R. This is performed using a path integral over the modes, which generate a quasi-associative algebra. The resulting models have a manifest U q (su( 2)) symmetry with a smooth limit q → 1, and satisfy positivity and twisted bosonic symmetry properties. A systematic way to calculate n-point correlators in perturbation theory is given. As examples, the 4-point correlator for a free scalar field theory and the planar contribution to the tadpole diagram in φ 4 theory are computed. The case of gauge fields is also discussed, as well as an operator formulation of scalar field theory in 2 q + 1 dimensions. An alternative, essentially equivalent approach using associative techniques only is also presented. The proposed framework is not restricted to two dimensions.