## Abstract

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.

Original language | English |
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Pages (from-to) | 365-433 |

Number of pages | 69 |

Journal | Journal of High Energy Physics |

Volume | 8 |

Issue number | 1 |

Publication status | Published - 1 Jan 2004 |

## Keywords

- Matrix Models
- Non-Commutative Geometry
- Renormalization Regularization and Renormalons