非交换 R^d 上量子场论的重整化, I. 标量场
高能物理 - 理论
2009-10-31 v4
摘要
非交换费曼图是一种带状图,可以画在带边界的亏格 二维曲面上。我们用拓扑术语表述了非交换费曼图的一般收敛定理,并在标量场论中的某些图类上予以证明。我们提出了 Bogoliubov-Parasiuk 递推减除公式的非交换类比,并证明了来自类 的减除图满足收敛定理的条件。对于 上的通用标量非交换量子场论,类 小于该理论中全部图的类。这使得非交换场论的微扰可重整化问题悬而未决。我们评论了超对称如何改善这一状况,并建议非交换的 Wess-Zumino 模型类比是可重整化的。
引用
@article{arxiv.hep-th/9911098,
title = {Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars},
author = {Iouri Chepelev and Radu Roiban},
journal= {arXiv preprint arXiv:hep-th/9911098},
year = {2009}
}
备注
Latex, 31 pages, many postscript figures; v2: A false statement in section 4.2 fixed and 3 figures added. The concluding section modified: scalar NQFT is not renormalizable. An argument about renormalizability of Wess-Zumino model added in the concluding section. References added; v3: Title of figure 15 changed. Typos corrected. A reference added; v4: Improved definition of index j and some clarifying comments. Added references. Statements on non-renormalizability softened at the referee's request