  We consider a quantum-electrodynamic problem of the spontaneous emission from
a two-dimensional (2D) emitter, such as a quantum well or a 2D semiconductor,
placed in a quasi-2D waveguide or cavity with subwavelength confinement in one
direction. We apply the Heisenberg-Langevin approach which includes dissipation
and fluctuations in the electron ensemble and in the electromagnetic field of a
cavity on equal footing. The Langevin noise operators that we introduce do not
depend on any particular model of dissipative reservoir and can be applied to
any dissipation mechanism. Moreover, our approach is applicable to
nonequilibrium electron systems, e.g. in the presence of pumping, beyond the
applicability of the standard fluctuation-dissipation theorem. We derive
analytic results for simple but practically important geometries: strip lines
and rectangular cavities. Our results show that a significant enhancement of
the spontaneous emission, by a factor of order 100 or higher, is possible for
quantum wells and other 2D emitters in a subwavelength cavity.
