Related papers: The minimal length: a cut-off in disguise?
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…
The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal…
String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle.…
Phenomenological studies of quantum gravity have proposed a modification of the commutator between position and momentum in quantum mechanics so to introduce a minimal uncertainty in position in quantum mechanics. Such a minimal uncertainty…
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be…
Many modern theories which try to unify gravity with the Standard Model of particle physics, as e.g. string theory, propose two key modifications to the commonly known physical theories: i) the existence of additional space dimensions; ii)…
The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar…
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations…
The narrow and subtle difference between the Hilbert spaces of operators corresponding to the purely quantum mechanical momentum and the generalized momentum that includes minimal length effects is polished. Additionally, the existence of…
In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal obserlvable length), as a fundamental part of the quantization process of the electrodynamical…
The dynamics of a particle in a gravitational quantum well is studied in the context of nonrelativistic quantum mechanics with a particular deformation of a two-dimensional Heisenberg algebra. This deformation yields a new short-distance…
Phenomenological models of quantum gravity often consider the existence of some form of minimal length. This feature is commonly described in the context of quantum mechanics and using the corresponding formalism and techniques. Although…
The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients…
Modifications of Heisenberg's uncertainty relations have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change…
It is commonly accepted that the combination of quantum mechanics and general relativity gives rise to the emergence of a minimum uncertainty both in space and time. The arguments that support this conclusion are mainly based on…
During the last two decades or so much effort has been devoted to the discussion of quantum mechanics (QM) that in some way incorporates the notion of a minimum length. This upsurge of research has been prompted by the modified uncertainty…
Deformations of the canonical commutation relations lead to non-Hermitian momentum and position operators and therefore almost inevitably to non-Hermitian Hamiltonians. We demonstrate that such type of deformed quantum mechanical systems…
Broad arguments indicate that quantum gravity should have a minimal length scale. In this essay we construct a minimum length model by generalizing the time-position and energy-momentum operators while keeping much of the structure of…
The existence of a minimal measurable length is a common feature of various approaches to quantum gravity such as string theory, loop quantum gravity and black-hole physics. In this scenario, all commutation relations are modified and the…
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…