Gaussian basis expansion of the QED light cone Hamiltonian

We obtain a rigorous transformation from a plane-wave basis expansion of the fields to a Gaussian basis expansion. We then use this transformation to derive the Gaussian basis representation of the normal mode sector of the discretized light cone Hamiltonian for QED. This is advantageous because it allows one to fully formulate a bound state problem using a plane-wave basis but then transform to the Gaussian basis for the numerical implementation.