  The quantum theory of Brownian motion is discussed in the Schwinger version
wherein the notion of a coordinate moving forward in time $x(t)$ is replaced by
two coordinates, $x_+(t)$ moving forward in time and $x_-(t)$ moving backward
in time. The role of the doubling of the degrees of freedom is illustrated for
the case of electron beam two slit diffraction experiments. Interference is
computed with and without dissipation (described by a thermal bath). The notion
of a dissipative interference phase, closely analogous to the Aharonov-Bohm
magnetic field induced phase, is explored.
