  Exciton problem is solved in the two-dimensional Dirac model with allowance
for strong electron-hole attraction. The exciton binding energy is assumed
smaller than but comparable to the band gap. The exciton wavefunction is found
in the momentum space as a superposition of all four two-particle states
including electron and hole states with both positive and negative energies.
The matrix element of exciton generation is shown to depend on the additional
components of the exciton wavefunction. Both the Coulomb and the Rytova-Keldysh
potentials are considered. The dependence of the binding energy on the coupling
constant is analyzed for the ground and first excited exciton states. The
binding energy and the oscillator strength are studied as functions of the
environmental-dependent dielectric constant for real transition metal
dichalcogenide monolayers. We demonstrate that the multicomponent nature of the
exciton wavefunction is crucial for description of resonant optical properties
of two-dimensional Dirac systems.
