We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal star-product. Explicit results are presented for all Green's functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed non-perturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an infinite-dimensional noncommutative algebra. © SISSA/ISAS 2004.
|Number of pages||69|
|Journal||Journal of High Energy Physics|
|Publication status||Published - 1 Jan 2004|
- Matrix Models
- Non-Commutative Geometry
- Renormalization Regularization and Renormalons