On the physics of the minimal length: The question of gauge invariance

Chang, Lay Nam; Minić, Djordje; Roman, Ahmed; Sun, Chen; Takeuchi, Tatsu

doi:10.1142/s0217751x1630012x

Cited by 12 publications

(6 citation statements)

References 91 publications

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“…At the end of T-dualization procedure background fields depend on ∆V , defined as line integral. Nonlocality has been become very important issue in the quantum mechanical considerations [45].…”

Section: Jhep03(2019)136mentioning

confidence: 99%

Directly from H-flux to the family of three nonlocal R-flux theories

Nikolić

Obrić

2019

J. High Energ. Phys.

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In this article we consider T-dualization of the 3D closed bosonic string in the weakly curved background-constant metric and Kalb-Ramond field with one nonzero component, B xy = Hz, where field strength H is infinitesimal. We use standard and generalized Buscher T-dualization procedure and make T-dualization starting from coordinate z, via y and finally along x coordinate. All three theories are nonlocal, because variable ∆V , defined as line integral, appears as an argument of background fields. After the first T-dualization we obtain commutative and associative theory, while after we Tdualize along y, we get, κ-Minkowski-like, noncommutative and associative theory. At the end of this T-dualization chain we come to the theory which is both noncommutative and nonassociative. The form of the final T-dual action does not depend on the order of Tdualization while noncommutativity and nonassociativity relations could be obtained from those in the x → y → z case by replacing H → −H.

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Section: Jhep03(2019)136mentioning

confidence: 99%

Directly from H-flux to the family of three nonlocal R-flux theories

Nikolić

Obrić

2019

J. High Energ. Phys.

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“…Theoretical foundations: One of the common features of various approaches to quantum gravity is the concept of minimal length [31][32][33][34][35][36]. Naively, the presence of length or mass scales contradicts relativity (different boosted observers would see different minimal lengths/times, contradicting the very concept of "minimal length/time") [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Infrared Properties of Quantum Gravity: UV/IR Mixing, Gravitizing the Quantum -- Theory and Observation

Berglund¹,

Freidel²,

Hübsch³

et al. 2022

Preprint

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We discuss the possible appearance of several rather exotic phenomena in quantum gravity, including UV/IR mixing, novel modifications of infrared phenomenology that extend effective field theory approaches, and the relaxation of the usual notions of locality. We discuss the relevance of such concepts in quantum gravity for quantum information science, cosmology and general quantum gravity phenomenology.

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“…Therefore, understanding the maximal wavelength as the radius of the cosmological horizon, it combines quantum gravitational as well as horizon-induced effects. Despite a number of open issues such as the inverse soccer ball problem [28], the classical limit [77,78], friction with the second law of thermodynamics [79], combination with gauge symmetries [80] or, depending on the relativistic completion, deformation [81] or straight breaking [82] of Lorentz-invariance, this endeavour has lead to manifold phenomenological applications [83][84][85][86][87][88][89][90][91][92][93][94][95][96][97].…”

Section: Introductionmentioning

confidence: 99%

Towards quantum Mechanics on the curved cotangent bundle

Wagner¹

2021

Preprint

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The minimum length paradigm, a cornerstone of quantum gravity phenomenology, and quantum theories on nontrivial momentum space have been brought into explicit correspondence, recently. However, owing to the fact that coordinate transformations introduce additional positiondependence to the otherwise solely momentum-dependent metric, there is no fully consistent formulation of these theories beyond Cartesian coordinates and, in particular, no position representation. This paper is intended to take the first steps in bridging this gap by promoting the measure of the Hilbert space scalar product to an operator and merging it, by analogy with geometric quantization, with the wave functions. Correspondingly, we find a natural action of the position and momentum operators on the resulting wave densities in both of their representations, as well as the free particle-Hamiltonian and the geodesic distance. These reduce to their counterparts in DeWitt's approach to quantum mechanics on curved spaces in the corresponding circumstances. We apply the formalism perturbatively in a Riemann normal coordinate-like expansion, with curvature in position and momentum space simultaneously, to the isotropic harmonic oscillator and the hydrogen-like atom. Interestingly, under suitable choice of operator ordering, the former retains its symmetry with respect to exchange of positions and momenta, making it impossible to distinguish positionfrom momentum space-curvature. We thus obtain a true instantiation of Born reciprocity on the curved cotangent bundle.

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On the physics of the minimal length: The question of gauge invariance

Abstract: In this note we discuss the question of gauge invariance in the presence of a minimal length. This contribution is prepared for the celebration of the 60th anniversary of the Yang–Mills theory.

Cited by 12 publications

References 91 publications

Directly from H-flux to the family of three nonlocal R-flux theories

Directly from H-flux to the family of three nonlocal R-flux theories

Infrared Properties of Quantum Gravity: UV/IR Mixing, Gravitizing the Quantum -- Theory and Observation

Towards quantum Mechanics on the curved cotangent bundle

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