Dynamical Features of Maggiore's Generalised Commutation Relations

TL;DR

This paper investigates the dynamical implications of Maggiore's generalized commutation relations, deriving modifications to black body radiation, analyzing statistical mechanics, and exploring early universe evolution, highlighting their generic dependence on the Hamiltonian.

Contribution

It provides a systematic analysis of how Maggiore's generalized commutation relations influence physical phenomena, extending previous work and emphasizing their generic features.

Findings

Generalized Planck's law derived for black body spectrum

Statistical mechanics of free particles analyzed under the new relations

Early universe evolution exhibits non-trivial features depending on the Hamiltonian

Abstract

We study the dynamical features of Maggiore's generalised commutation relations. 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.