  We develop a general technique, based on a Bochner-type identity, to estimate
spectral gaps of a class of Markov operator. We apply this technique to various
interacting particle systems. In particular, we give a simple and short proof
of the diffusive scaling of the spectral gap of the Kawasaki model at high
temperature. Similar results are derived for Kawasaki-type dynamics in the
lattice without exclusion, and in the continuum. New estimates for Glauber-type
dynamics are also obtained.
