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

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.

13 pages, 6 figures

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• Generalized Uncertainty Principle, Classical Mechanics, and General Relativity
• Heuristic derivation of Casimir effect in minimal length theories
• Modified commutators are not sufficient to determine a quantum gravity minimal length scale
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