The minimal length is physical

TL;DR

This paper clarifies misconceptions in quantum gravity related to the minimal length concept, emphasizing the importance of distinguishing between algebraic deformations and operator representations to maintain physical consistency.

Contribution

It corrects recent misunderstandings by clarifying the distinction between algebraic deformations and operator representations in the context of minimal length in quantum gravity.

Findings

Misconceptions stem from confusing perturbative and non-perturbative methods.

The minimal length is representation-independent and physically meaningful.

Clarifies the proper mathematical framework for quantum gravity phenomenology.

Abstract

In this paper, we clarify a foundational loose end affecting the phenomenological approach to quantum gravity centered around the generalization of Heisenberg uncertainty principle. This misconception stems from a series of recently published works in which perturbative and non-perturbative methods are confused, thereby resulting in a blurring of the distinction between changes in the deformed algebra and changes in the representation of operators. Accordingly, this reasoning would render the existence of a minimal length representation-dependent, and thus unphysical.