Continuous Quantum Nondemolition Measurements Of A Particle In Electromagnetic And Gravitational Fields

We discuss the theory of continuous quantum measurements (CQM), andthe de?nition and essential principals of quantum nondemolition (QND)measurements are reviewed. A continuously measured quantum systemcan be described by restricted path integral (RPI) or equivalently by non-Hermitian Hamiltonians. The measured system is then regarded as anopen system, and the in?uence of the environment is taken into accountby restricting the path integral or by inclusion of an imaginary part in theHamiltonian. Thus we obtain a set of quantum nondemolition variablesfor the case in which a charged particle moves in the electromagneticand gravitational ?elds of a spherical body. Furthermore, we considerthe continuous monitoring of these nondemolition parameters, and cal-culate the corresponding propagators by means of RPI formalism. Usingthese results the probabilities associated with the possible measurementoutputs are evaluated.