  We present a new dynamical proof of the Thouless-Anderson-Palmer (TAP)
equations for the classical Sherrington-Kirkpatrick spin glass at sufficiently
high temperature. In our derivation, the TAP equations are a simple consequence
of the decay of the two point correlation functions. The methods can also be
used to establish the decay of higher order correlation functions. We
illustrate this by proving a suitable decay bound on the three point functions
from which we derive an analogue of the TAP equations for the two point
functions.
