  We consider an equilibrium birth and death type process for a particle system
in infinite volume, the latter is described by the space of all locally finite
point configurations on $\R^d$. These Glauber type dynamics are Markov
processes constructed for pre-given reversible measures. A representation for
the "carr\'e du champ" and "second carr\'e du champ" for the associate
infinitesimal generators $L$ are calculated in infinite volume and a
corresponding coercivity identity is derived. The latter is used to give
explicit sufficient conditions for the appearance and bounds for the size of
the spectral gap of $L$. These techniques are applied to Glauber dynamics
associated to Gibbs measure and conditions are derived extending all previous
known results. In the high temperature regime now potentials also with a
non-trivial negative part can be treated. Furthermore, a special class of
potentials is defined for which the size of the spectral gap is as least as
large as for the free system and, surprisingly, is independent of the activity.
This type of potentials should not show any phase transition for a given
temperature at any activity.
