Light-Cone Quantization and Renormalization of Large-N Scalar Matrix Models

We discuss the issue of renormalization and the derivation of effective interactions for light-cone Hamiltonians in the context of large-N scalar matrix models with $\Phi^3$ interactions. For various space-time dimensions $D \geq 3$, we deduce appropriate mass, coupling constant, and wavefunction renormalizations which are necessary for finiteness of the Hamiltonian at leading order. We also outline how higher order corrections may be derived within this framework, and discuss the relevance of this approach in the light-cone quantization of gauge theories.