Physics at very high energies (close to the Planck energy scale) is in the center of modern physics challenges. At the high energy scales, or equivalently very short distances, the very notion of spacetime acquires a complicated structure. In this scale, there are limitations on the complete resolution of adjacent points in spacetime manifold. While the effect of a minimal measurable length on algebraic structure of a free particle’s phase space has been studied in the literature, the simultaneous effects of minimal length and maximal momentum have not been explored in this subject so far. Here, we are going to fill this gap. We study some properties of the algebraic structure of quantum field theories in the presence of natural cutoffs as a minimal length and a maximal momentum in a free particle’s phase space. Especially, we pay attention on the phase space trajectories of systems in the presence of natural cutoffs.
