  In this work a family of quantum nondemolition variables for the case of a
particle caught in a Paul trap is obtained. Afterwards, in the context of the
so called restricted path integral formalism, a continuous measuring process
for this family of parameters is considered, and then the corresponding
propagators are calculated. In other words, the time evolution of a particle in
a Paul trap, when the corresponding quantum nondemolition parameter is being
continuously monitored, is deduced. The probabilities associated with the
possible measurement outputs are also obtained, and in this way new theoretical
results emerge, which could allow us to confront the predictions of this
restricted path integral formalism with the readouts of some future
experiments.
