  We present a technique for treating many particles moving inside a ballistic
interferometer, under the influence of a quantum-mechanical environment
(phonons, photons, Nyquist noise etc.). Our approach is based on solving the
coupled Heisenberg equations of motion of the many-particle system and the bath
and is inspired by the quantum Langevin method known for the Caldeira Leggett
model. It allows to study decoherence and the influence of the bath on other
properties of the interferometer. As a first application, we treat a fermionic
Mach-Zehnder interferometer. In particular, we discuss the dephasing rate and
present full analytical expressions for the leading corrections to the current
noise, brought about by the coupling to the quantum bath.
