On the quasi-position representation in theories with a minimal length

TL;DR

This paper reviews the challenges and misunderstandings in representing position in quantum models with a minimal length, clarifying issues related to the position operator in such theories.

Contribution

It provides a detailed analysis of the quasi-position representation in minimal length quantum models, clarifying conceptual and mathematical issues.

Findings

Identifies issues in the quasi-position representation

Clarifies the representation of the position operator

Highlights misunderstandings in minimal length models

Abstract

Quantum mechanical models with a minimal length are often described by modifying the commutation relation between position and momentum. Although this represents a small complication when described in momentum space, at least formally, the (quasi-)position representation acquires numerous issues, source of misunderstandings. In this work, we review these issues, clarifying some of the aspects of minimal length models, with particular reference to the representation of the position operator.