Many current and future experiments aim to observe the radio emission produced by air showers sourced from cosmic rays and neutrinos. Extensive simulations of these showers are required to optimize future experimental designs and to accurately reconstruct the parameters of detected events. Traditionally, the vector potential from every particle track in the shower is calculated separately for a given antenna position. This vector potential calculation is computationally expensive, and makes simulation of realistic showers (less thinning) inconvenient due to long computation times.\\

In this work, we present a novel, semi-analytical treatment of this calculation, whereby multiple tracks within a 4-Dimensional spacetime volume can be treated as one, weighted by the other tracks within the volume. Expensive calculations previously performed on a per-track basis need only to be calculated once for each volume, thereby reducing computation time and complexity. These 4-D volumes can be large while satisfying diffraction limits, capturing many tracks at once, with the number of contained tracks increasing with decreasing thinning (more realistic showers). This method has been shown to reproduce the results of full ZHAireS simulations in a fraction of the time while keeping the precision of the microscopic treatment.\\

We demonstrate the efficacy of this method by showing comparisons to full microscopic simulations for given shower geometries and highlighting the reduction in computational time and complexity. We discuss the use cases for this method and its limitations as well as future applications.