# On the relation between spin and angular momentum in the phase space of the four dimensional $\mathcal{N}=4$ super-Yang-Mills theory

Comments: 8 pages, 7 figures

We study the relation between the angular momentum and spin of the four dimensional $\mathcal{N}=4$ super-Yang-Mills theory in the direction of the standard coordinate. We show that it is possible to predict the angular momentum of a reference particle in the magnetic direction in the phase space of the four dimensional $\mathcal{N}=4$ super-Yang-Mills theory. This uncertainty principle is violated in the magnetic direction so that the calculations of the angular momentum are performed in the phase space of the four dimensional $\mathcal{N}=4$ super-Yang-Mills theory.