場の理論の基礎的諸問題の探求

对作者提出的一般费米子算符类的定域性进行了检验。关于定域性的证明还不完全，但已经证明了没有背景规范场的费米子算符是定域的。这表明，对于接近连续极限的足够弱的规范场，这些算符是局域的。与Ginsparg-Wilson算符有关的结果表明，Majorana费米子的定义并不一致。对于基于Ginsparg-Wilson算子的手征理论，CP对称性也是普遍破缺的。详细分析了CP破坏在全量子化理论中的意义，指出CP破坏可以被吸收到不含Higgs耦合的纯手征规范理论的路径积分的归一化因子中.对于以畴壁费米子定义的手征理论，作用能级上的C P破坏也是存在的，提出了一种避免格点上超对称理论的Leibniz规则破缺的可能方案.我们还证明了路径积分玻色化中的定域反项与规范理论中的定域反项是完全不同的，从而为路径积分玻色化的成功提供了依据。除上述内容外，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模型中心电荷的反常.然后我们详细说明了异常现象的性质。

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.