  A four-band exciton Hamiltonian is constructed starting from the
single-particle Dirac Hamiltonian for charge carriers in monolayer transition
metal dichalcogenides (TMDs). The angular part of the exciton wave function can
be separated from the radial part, in the case of zero center of mass momentum
excitons, by exploiting the eigenstates of the total exciton angular momentum
operator with which the Hamiltonian commutes. We explain why this approach
fails for excitons with finite center of mass momentum or in the presence of a
perpendicular magnetic field and present an approximation to resolve this
issue. We calculate the (binding) energy and average interparticle distance of
different excited exciton states in different TMDs and compare these with
results available in the literature. Remarkably, we find that the intervalley
exciton ground state in the $\mp K$ valley has angular momentum $j=\pm1$, which
is due to the pseudospin of the separate particles. The exciton mass and the
exciton Landau levels are calculated and we find that the degeneracy of exciton
states with opposite relative angular momentum is altered by a magnetic field.
