Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Bosso, Pasquale; Luciano, Giuseppe Gaetano

doi:10.1140/epjc/s10052-021-09795-1

Cited by 42 publications

(32 citation statements)

References 67 publications

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“…Analogous conclusion is found on a different context on[39] for the one-dimensional commutator [x, p] = i f (p).B. Anisotropic models…”

supporting

confidence: 74%

On the algebraic approach to GUP in anisotropic space

Gomes

2023

Preprint

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Motivated by current searches for signals of Lorentz symmetry violation in nature and recent investigations on generalized uncertainty principle (GUP) models in anisotropic space, in this paper we identify GUP models satisfying two criteria: (i) invariance of commutators under canonical transformations, and (ii) physical independence of position and momentum on the ordering of auxiliary operators in their definitions. Compliance of these criteria is fundamental if one wishes to unambiguously describe GUP using an algebraic approach but, surprisingly, neither is trivially satisfied when GUP is assumed within anisotropic space. As a consequence, we use these criteria to place important restrictions on what or how GUP models may be approached algebraically.

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“…Analogous conclusion is found on a different context on[39] for the one-dimensional commutator [x, p] = i f (p).B. Anisotropic models…”

supporting

confidence: 74%

On the algebraic approach to GUP in anisotropic space

Gomes

2023

Preprint

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“…There is an intense activity to find GUP-corrected physics. Besides the already cited work of [14,15,16,17], other important results that use different approaches are in [18,19,20]. A compelling example for this paper, for instance, is in [17] where it is found that the GUP-corrected Dirac equation, in any dimension, is…”

Section: Introductionmentioning

confidence: 89%

Shadows of new physics on Dirac materials, analog GUPs and other amusements

Iorio

Ivetić²,

Mignemi

et al. 2023

J. Phys.: Conf. Ser.

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We discuss here how, when higher-order effects in the parameter ℓ ℏ | p → | , related to the lattice spacing ℓ, are considered, pristine graphene, and other Dirac materials, can be used as tabletop systems where generalized commutation relations are naturally realized. Such generalized algebras of quantization, which lead to generalized versions of the Heisenberg uncertainty principle, are under intense scrutiny these days, as they could manifest a fundamental length scale of spacetime. Despite the efforts and the many intriguing results, there are no experimental signatures of any generalized uncertainty principle (GUP). Therefore, our results here, which tell how to use tabletop physical systems to test certain GUPs in analog experiments, should be of interest to practitioners of quantum gravity. We identify three different energy regimes that we call “layers”, where the physics is still of a Dirac type but within precisely described limits. The higher the energy, the more sensitive the Dirac system becomes to the effects of the lattice. Here such lattice plays the role of a discrete space where the Dirac quasi-particles live. With the goals just illustrated, we had to identify the mapping between the high-energy coordinates, X i , and the low-energy ones, x i , i.e., those measured in the lab. We then obtained three generalized Heisenberg algebras. For two of them we have the noticeable result that X i = x i , and for the third one we obtained an improvement with respect to an earlier work: the generalized coordinates expressed in terms of the standard phase space variables, X i (x, p), and higher order terms.

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“…The (dimensionless) deformation parameter β is not fixed by the theory, although investigation along this line is active both at theoretical [74][75][76][77][78][79] and experimental level [80][81][82][83]. Quite debated is also the issue of the sign of β, with arguments in favor of either positive [68,[70][71][72]76,77] or negative [73,78,84,85] β.…”

Section: Connecting Tsallis Thermostatistics and Generalized Uncertai...mentioning

confidence: 99%