On the quasi-position representation in theories with a minimal length. (English) Zbl 1481.83043
Summary: 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.
MSC:
| 83C45 | Quantization of the gravitational field |
| 93C65 | Discrete event control/observation systems |
| 81S07 | Uncertainty relations, also entropic |
| 81R60 | Noncommutative geometry in quantum theory |
Keywords:
quantum gravity phenomenology; minimal length; quantum mechanics; generalized uncertainty principleReferences:
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