  We present exact solutions of an energy spectrum of 2-interacting particles
in which they seem to be relativistic fermions in 2+1 space-time dimensions.
The 2x2 spinor equations of 2-interacting fermions through general central
potential were separated covariantly into the relative and center of mass
coordinates. First of all, the coupled first order differential equations
depending on radial coordinate were derived from 2x2 spinor equations. Then, a
second order radial differential equation was obtained and solved for Coulomb
interaction potential. We apply our solutions to exciton phenomena for a
free-standing monolayer medium. Since we regard exciton as isolated
2-interacting fermions in our model, any other external effect such as
substrate was eliminated. Our results show that the obtained binding energies
in our model are in agreement with the literature. Moreover, the decay time of
an exciton was found out spontaneously in our calculations.
