  We develop a bosonization formalism that captures non-perturbatively the
interaction effects on the $\mathbf{Q}=0$ continuum of excitations of nodal
fermions above one dimension. Our approach is a natural extension of the
classic bosonization scheme for higher dimensional Fermi surfaces to include
the $\mathbf{Q}=0$ neutral excitations that would be absent in a single-band
system. The problem is reduced to solving a boson bilinear Hamiltonian. We
establish a rigorous microscopic footing for this approach by showing that the
solution of such boson bilinear Hamiltonian is exactly equivalent to performing
the infinite sum of Feynman diagrams associated with the Kadanoff-Baym
particle-hole propagator that arises from the self-consistent Hartree-Fock
approximation to the single particle Green's function. We apply this machinery
to compute the interaction corrections to the optical conductivity of 2D Dirac
Fermions with Coulomb interactions reproducing the results of perturbative
renormalization group at weak coupling and extending them to the strong
coupling regime.
