General Dynamical Features of the Generalised Commutation

We study the dynamical features of the generalised commutation relations, derived uniquely by Maggiore. We focus on their generality and, in particular, their dependence on the Hamiltonian H . We derive the generalisation of the Planck’s law for black body spectrum, study the statistical mechanics of free particles, and study the early universe evolution which now exhibits non trivial features. We find that the dynamical features, found here and in our earlier work, are all generic and vary systematically with respect to the asymptotic growth of the Hamiltonian H .