場の理論の基礎的諸問題の探求

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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.