Potential-based integral equations are being explored to develop numerical methods that avoid low frequency breakdown issues and are better suited to couple to quantum physics computations. Important classes of quantum electrodynamics problems are typically formulated in the radiation gauge, leading to interest in efficient numerical solutions able to be performed directly in this gauge. This work presents time domain integral equations for penetrable regions that are developed in the radiation gauge. An appropriate marching-on-in-time discretization scheme is developed that fully conforms to the spatial and temporal Sobolev space properties of the integral equations. It is shown that following this approach leads to a discrete system with improved stability properties that produces accurate results down to very low frequencies. The accuracy and stability of this formulation at low frequencies are shown through numerical results.
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