Regularization and Renormalization of Quantum Field Theories on Noncommutative Spaces
- 10.2991/jnmp.2004.11.s1.2How to use a DOI?
We first review regularization methods based on matrix geometry which provide an ultraviolet cut-off for scalar fields respecting the symmetries. Sections of bundles over the sphere can be quantized, too. This procedure even allows to regularize supesymmetry without violating it. Recently, this work was extended to include quantum group covariant regularizations. In a second part recent attempts to renormalize four-dimensional deformed quatum field theory models are reviewed. For scalar models the well-known UV/IR-mixing does not allow to use standard techniques. The same applies to the Yang-Mills model in four dimensions. Only additional symmetry, as it occurs in the Wess-Zumino model, may allow to avoid this problem. There was some hope that circumventing UV/IR-mixing by application of the Seiberg-Witten map one can achieve renormalizability of noncommutative field thories. Although the photon self-energy is renormalizable to all orders, -expanded noncommutative QED was shown to be not renormalizable, thus ruling out this aproach as well.
- © 2006, the Authors. Published by Atlantis Press.
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Cite this article
TY - JOUR AU - Harald Grosse AU - Raimar Wulkenhaar PY - 2004 DA - 2004/10/01 TI - Regularization and Renormalization of Quantum Field Theories on Noncommutative Spaces JO - Journal of Nonlinear Mathematical Physics SP - 9 EP - 20 VL - 11 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2004.11.s1.2 DO - 10.2991/jnmp.2004.11.s1.2 ID - Grosse2004 ER -