  We study massless scalar theory with the quartic self-interacting term far
away from and near to evaporating and spherically symmetric black hole. We
propose a principle of how to define the physical notion of particle in curved
space-time. Employing this definition, we compute one-loop correction to the
self-energy and coupling constant of the scalar field near the horizon in the
freely-falling frame. We find that the coupling constant becomes slightly
stronger near to the horizon. We also find that the term in the 2-point
function that is (partially) responsible for the black-hole evaporation
corresponds to the sub-leading correction to the Feynman propagator whose pole
structure is of the leading order.
