Minimal and maximal lengths from position-dependent noncommutativity

Abstract

Fring and al in their paper entitled "Strings from position-dependent noncommutativity" have introduced a new set of noncommutative space commutation relations in two space dimensions. It had been shown that any fundamental objects introduced in this space-space non-commutativity are string-like. Taking this result into account, we generalize the seminal work of Fring and al to the case that there is also a maximal length from position-dependent noncommutativity and minimal momentum arising from generalized versions of Heisenberg's uncertainty relations. The existence of maximal length is related to the presence of an extra, first order term in particle's length that provides the basic difference of our analysis with theirs. This maximal length breaks up the well known singularity problem of space time. We establish different representations of this noncommutative space and finally we study some basic and interesting quantum mechanical systems in these new variables.

25 pages

References in corpus (6)

• Discreteness of Space from the Generalized Uncertainty Principle
• GUP parameter from quantum corrections to the Newtonian potential
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications
• Covariant realizations of kappa-deformed space
• On the modification of Hamiltonians' spectrum in gravitational quantum mechanics
• Deformation of the Wheeler-DeWitt Equation