Radiance fields, including their recent efficient forms such as 3D Gaussian Splatting and Sparse Voxels, have revolutionized photorealistic 3D scene visualization by enabling high-fidelity reconstruction of complex environments, making them a natural match for light field displays. However, integrating these technologies presents significant computational challenges, as light field displays require many high-resolution renderings from slightly shifted viewpoints, while radiance fields rely on computationally intensive volume rendering, which is intractable to achieve real-time speeds even with efficient scene representations. In this paper, we propose a unified and efficient framework for real-time radiance field rendering on light field displays. Rather than re-rendering each view independently, our method converts the input radiance field into shared intermediate sweeping planes that can be efficiently composited into dense light-field views in a single pass. Our method prioritizes shared, non-directional plane caching for real-time performance, trading fine view-dependent color effects for a modest increase in intermediate memory usage. Our framework generalizes across different scene representations without retraining and avoids repeated computation across views. We further demonstrate a real-time interactive application on a Looking Glass display, achieving 200+ FPS at 512p across 45 rendered views and enabling seamless, immersive 3D interactive viewing experiences. On standard benchmarks, our method achieves up to 22× speedup compared to independently rendering each view, while largely preserving image quality.