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

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.

Automated summary

Quantum mechanical models with a minimal length often involve modifying the relationship between position and momentum. While this is a minor complication in momentum space, the representation in (quasi-)position space poses many issues and leads to misunderstandings. This work reviews and clarifies some aspects of minimal length models, focusing on the representation of the position operator.