The numerically observed approximate functional forms for the transverse and longitudinal-momentum proportional (LP) Gram-Schmidt Lyapunov modes have been studied for some time. We construct a field theory for a system where the number of particles is large enough so the Lyapunov mode contributions from each particle can be considered to change continuously with particle position, whose solution gives the observed functional forms for all modes. The wave equations obtained as solutions of the field theory are derived either phenomenologically or from the exact dynamics of two-dimensional hard particles. The wave speed of the LP modes is predicted to reasonable accuracy for a range of densities and system sizes.