Hilbert Space Representation of the Minimal Length Uncertainty Relation

TL;DR

This paper explores the quantum mechanical framework underlying the minimal length uncertainty relation, which is significant in quantum gravity and string theory, by analyzing its mathematical structure in detail.

Contribution

It provides a detailed analysis of the quantum mechanical structure that underpins the minimal length uncertainty relation, advancing theoretical understanding.

Findings

Detailed quantum structure of minimal length uncertainty relation elucidated

Mathematical framework for minimal length in quantum mechanics developed

Implications for quantum gravity and string theory discussed

Abstract

The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements. Here we study in full detail the quantum mechanical structure which underlies this uncertainty relation.