While there is a growing consensus that the pairing
interaction in the cuprates arises from short range Coulomb
interactions between electrons, the precise nature of the pairing
interaction remains controversial. This is the case even among those
that agree that the Hubbard and t-J models contain the essential
physics of the problem. Central to this controversy is the question
of whether there is a "pairing glue" . This is a question regarding
the dynamics of the pairing interaction. If the pairing interaction
arises from the exchange of spin-fluctuations, its dynamics will
reflect the frequency spectrum associated with inelastic magnetic
neutron scattering. This frequency scale is small compared with U or
the bare bandwidth and one speaks of a retarded, spin-fluctuation
mediated "pairing glue". Alternatively, in the RVB approach, as noted
by P.W.Anderson, the exchange coupling J, which attracts electrons
of opposite spins on neighboring sites is the result of states of
very high energy. In this case, the corresponding interaction has
only high-frequency dynamics, so it is unrelated to a "glue". In this
talk, we will discuss what numerical calculations tell us about the
dynamics of the pairing interaction in the Hubbard and t-J models and
review what is presently being seen experimentally.
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