Farewell to instantons

This lecture shows that it is doubtful that the instanton can be used in QCD to explain color confinement and dynamical symmetry breaking with fermion mass generation, or can resolve the U(1)problem. The instanton may even be irrelevant to the structure of QCD altogether. It is shown that for massless fields the ratio of instanton to free field determinant depends upon the infrared and ultraviolet cutoff if the computation is carried out in flat space R /SUP n/ or over the sphere/S /SUP n/ respectively--an important point for understanding the role of the instanton in pure QCD4, for example. It is also shown that for massless fields the value of the determinant depends upon the boundary conditions used to define the operator. This second conclusion indicates that massless fermions have been mistreated since care has not been taken to choose the physically correct definition of the fermion operator