Field Theory on the q-deformed Fuzzy Sphere II: Quantization

Details Field Theory on the q-deformed Fuzzy Sphere II: Quantization Field Theory on the q-deformed Fuzzy Sphere II: Quantization

2001-03-20

arxiv.org/abs/hep-th/0103164v1

J.Geom.Phys. 43 (2002) 205-240

Physics

High Energy Physics

High Energy Physics - Theory

LaTex file, 44 pages

Scientific paper

10.1016/S0393-0440(02)00023-2

We study the second quantization of field theory on the q-deformed fuzzy sphere for real q. This is performed using a path-integral over the modes, which generate a quasiassociative 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 \phi^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 2 dimensions.

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