Large hyper-volume visualization is required by today physic and is still a research area in scientific visualization. Especially, the interactive exploration of datasets remains highly challenging as soon as the data size exceeds a certain threshold. We describe in this paper an hyperslicing-based interactive visualization technique designed to explore at real-time frame rates large hyper-volumetric 4D scalar fields (i.e. datasets beyond 16GB) defined on regular structured grids. The key issue consists in coupling the visualization with a new efficient data representation scheme, in such a way that it overcomes the different steps of scientific visualization, namely simulation post-processing, visualization preprocessing and finally interactive display. By introducing a hierarchical finite element representation, we show that our technique allows users to explore the full dataset at real-time frame-rates on low-end PCs. We demonstrate the effectiveness of our technique on the interactive exploration of 4D phases space particle beams, resulting from numerical semi-Lagrangian simulations.