場の理論の基礎的諸問題の探求

研究了作者提出的一般费米子算子类的局部性。局部性的证明尚未完成，但证明了没有背景规范场的费米子算子是局部性的。这表明对于接近连续体极限的足够弱的规范场，算符是局部的。在与Ginsparg-Wilson算子的联系中，证明了马约拉纳费米子的定义并不一致。此外，基于Ginsparg-Wilson算子的手性理论一般也会破坏CP对称性。本文还详细分析了完全量子化理论中C - P违和的含义，并证明了在没有希格斯耦合的纯手性规范理论中，C - P违和可以被吸收到路径积分的归一化因子中。在作用能级上的cp违背也存在于由域壁费米子定义的手性理论中。提出了一种避免格上超对称理论的莱布尼茨规则被打破的可能处方。我们还证明了路径积分玻色子化中的局部计数器项与规范理论中的局部计数器项完全不同，从而为路径积分玻色子化的成功提供了基础。除了上述问题外，我们还利用路径积分的超场公式推导了二维N=(1,1)超对称Wess-Zumino模型的中心电荷异常。然后我们详细地澄清了异常的性质。

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.