  The techniques employed to solve the interaction of a detector and a quantum
field typically require perturbation methods. We introduce mathematical
techniques to solve the time evolution of an arbitrary number of detectors
interacting with a quantum field. Our techniques apply to harmonic oscillator
detectors and can be generalized to treat detectors modeled by quantum fields.
Since the interaction Hamiltonian we introduce is quadratic in creation and
annihilation operators, we are able to draw from continuous variable techniques
commonly employed in quantum optics.
