  A general treatment of the quantum Zeno and anti-Zeno effects is presented
which is valid for an arbitrary system-environment model in the weak
system-environment coupling regime. It is shown that the effective lifetime of
a quantum state that is subjected to repeated projective measurements depends
on the overlap of the spectral density of the environment and a generalized
`filter function' which in turn depends on the system state that is repeatedly
being prepared, the measurement interval, the system parameters, the
system-environment coupling, and the environment correlation function. This
general framework is then used to study explicitly the Zeno to anti-Zeno
crossover behavior for the spin-boson model where a single two-level system is
coupled to a bosonic environment. It is shown that our framework reproduces
results for the usual population decay case as well as for the pure dephasing
model, while at the same time allowing us to study the Zeno to anti-Zeno
transition when both decay and dephasing take place. These results are then
extended to many two-level systems coupled collectively to the bosonic
environment to show that the distinction between the Zeno and anti-Zeno effects
becomes more pronounced as the number of two-level systems increases.
