  In the thesis, first, the cancellation of infrared divergences in QED is
reviewed. Next, two examples in QCD, the quark-quark scattering and the
quark-gluon scattering are examined at one loop, from which the importance of
Ward-Takahashi identities becomes manifest for the cancellation to occur. The
factorization of infrared divergences in QCD is proved at all orders, by full
usage of the Ward-Takahashi identities. In these proofs, the axial gauge
condition is used. The cancellation of infrared divergences in QCD occurs among
the gauge invariant set of graphs. In this way, the low energy theorem of F. E.
Low, for emission of one or two soft gluons, are proved at all orders. From
this, the differential equation controlling the infrared divergences in QCD is
derived. In QCD, the coupling constant renormalization introduces the other
infrared divergence, which is governed by the beta-function in the pure
Yang-Mills theory. In the Epilogue 2022, a motivation for recently translating
the thesis in English is briefly stated.
