場の理論の基礎的諸問題の探求

场论基本问题的探索

基本信息

批准号：
13640266
负责人：
FUJIKAWA Kazuo
金额：
$ 1.98万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

项目摘要

The locality of the general class of fermion operators proposed by the author was examined. The proof of the locality is not complete yet, but it was proved that the fermionic operators without the background gauge field are local. This suggests that the operators are local for a sufficiently weak gauge field which is close to the continuum limit.In connection with the Ginsparg-Wilson opearators, it was shown that the Majorana fermions are not defined consistently. Also the CP symmetry is generally broken for the chiral theory based on the Ginsparg-Wilson opearators. The implications of the C P violation in the fully quantized theory were also analyzed in detail, and it was shown that the C P violation can be absorbed into the normalization factors of path integrals for pure chiral gauge theory without Higgs couplings. The C P violation in the action level persists also for the chiral theory defined in terms of the domain-wall fermions.A possible prescription to avoid the breaking of the Leibniz rule for the supersymmetyric theory on the lattice is suggested. We also shown that the local counter terms in the path integral bosonization is completely different from the local counter term in the gauge theory, and thus gave a basis for the success of the path integral bosonization. In addition to the above topics, we have also derived the anomaly in the central charge for a two-dimensional N=(1,1) supersymmetric Wess-Zumino model by means of the superfield formulation of path integral. We then claified the nature of the anomaly in detail.

检查了作者提出的一般类费米子算子的局部性。局域性的证明尚未完成，但已经证明了没有背景规范场的费米子算子是局域的。这表明对于接近连续介质极限的足够弱的规范场来说，算子是局域的。结合 Ginsparg-Wilson 算子，结果表明马约拉纳费米子的定义不一致。此外，基于 Ginsparg-Wilson 算子的手性理论通常会破坏 CP 对称性。详细分析了C P 违背在全量子化理论中的含义，结果表明，对于没有希格斯耦合的纯手性规范理论，C P 违背可以被吸收到路径积分的归一化因子中。对于用畴壁费米子定义的手性理论来说，作用能级中的 C P 违规也持续存在。提出了一种避免晶格超对称理论莱布尼茨规则被破坏的可能方案。我们还证明了路径积分玻色化中的局部反项与规范理论中的局部反项完全不同，从而为路径积分玻色化的成功奠定了基础。除上述主题外，我们还利用路径积分的超场公式导出了二维N=(1,1)超对称Wess-Zumino模型的中心电荷反常现象。然后我们详细阐明了异常的性质。