Relativistic Dynamics with Noncanonical Positions

Abstract

For any Hamiltonian $H$ having vanishing Poisson brackets with the total momentum $\overrightarrow{\mathrm{P}}$ and angular momentum $\overrightarrow{\mathrm{J}}$, it is always possible to construct boost operators $\overrightarrow{\mathrm{K}}$ having the correct Poisson brackets with all the other generators of the Poincaré group. Thus the existence of dynamical variables satisfying the algebra of the Poincaré group generators is not in itself a guarantee of Lorentz invariance.