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Noncommutative quantum mechanics on the plane has been widely studied in the literature. Here, we consider the problem using Isham's canonical group quantization scheme for which the primary object is the symmetry group that underlies the…

Mathematical Physics · Physics 2018-02-08 Mohd Faudzi Umar , Nurisya Mohd Shah , Hishamuddin Zainuddin

We consider the $\varrho$-Minkowski spacetime, a model with linear noncommutativity involving the time and the azimuthal angle. We study its quantum symmetries, the $\varrho$-Poincar\'e quantum group, and analyse the concepts of…

High Energy Physics - Theory · Physics 2022-11-09 Fedele Lizzi , Luca Scala , Patrizia Vitale

There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which…

General Relativity and Quantum Cosmology · Physics 2008-11-26 T. P. Singh

Relativistic deformed kinematics leads to a loss of the absolute locality of interactions. In previous studies, some models of noncommutative spacetimes in a two-particle system that implements locality were considered. In this work, we…

High Energy Physics - Theory · Physics 2025-04-07 J. J. Relancio

Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…

Mathematical Physics · Physics 2013-11-20 V. G. Kupriyanov

We present a simple algebraic argument for the conclusion that the low energy limit of a quantum theory of gravity must be a theory invariant, not under the Poincare group, but under a deformation of it parameterized by a dimensional…

High Energy Physics - Theory · Physics 2009-11-10 Giovanni Amelino-Camelia , Lee Smolin , Artem Starodubtsev

Continuous symmetries generated with observables of a quantum theory in the Minkowski spacetime are discussed. An example of an originated in this way algebra of observables is the algebra of observables of the canonical quantum theory,…

Mathematical Physics · Physics 2008-07-17 V. V. Khruschov

It is often expected that one cannot treat spacetime as a continuous manifold as the Planck scale is approached, because of to possible effects due to a quantum theory of gravity. There have been several proposals to model such a deviation…

General Relativity and Quantum Cosmology · Physics 2023-01-23 Andrea Bevilacqua

The Poincar\'e sector of a recently deformed conformal algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, the symmetries of a new relativistic theory with two observer-independent…

High Energy Physics - Theory · Physics 2016-11-09 Nicola Rossano Bruno

In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to a quantum structure with new properties. A possible way to take into account these quantum effects is through a noncommutativity of…

High Energy Physics - Theory · Physics 2023-07-25 Giulia Gubitosi , Fedele Lizzi , José Javier Relancio , Patrizia Vitale

Non-commutative spacetime and quantum groups have been argued to capture non-classical features of spacetime and its symmetries in the low-energy limit of quantum gravity. In this letter, we show that employing the $SU_q(2)$ quantum group…

Quantum Physics · Physics 2026-05-29 Vittorio D'Esposito , Giuseppe Fabiano , Domenico Frattulillo

We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical…

High Energy Physics - Theory · Physics 2009-11-11 Xavier Calmet , Michele Selvaggi

The realization that forthcoming experimental studies, such as the ones planned for the GLAST space telescope, will be sensitive to Planck-scale deviations from Lorentz symmetry has increased interest in noncommutative spacetimes in which…

High Energy Physics - Theory · Physics 2009-11-07 Giovanni Amelino-Camelia , Francesco D'Andrea , Gianluca Mandanici

Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of…

General Relativity and Quantum Cosmology · Physics 2009-10-31 R. Aldrovandi , A. L. Barbosa , L. C. B. Crispino , J. G. Pereira

In this letter we provide an invariant characterization for all spacetimes with all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives vanishing except those zeroth order curvature invariants…

General Relativity and Quantum Cosmology · Physics 2013-03-01 David McNutt

The dissertation presents possibilities of applying noncommutative spacetimes description, particularly kappa-deformed Minkowski spacetime and Drinfeld's deformation theory, as a mathematical formalism for Doubly Special Relativity theories…

Mathematical Physics · Physics 2011-12-23 Anna Pachoł

In the presence of a cosmological constant, ordinary Poincare' special relativity is no longer valid and must be replaced by a de Sitter special relativity, in which Minkowski space is replaced by a de Sitter spacetime. In consequence, the…

General Relativity and Quantum Cosmology · Physics 2009-11-13 R. Aldrovandi , J. P. Beltran Almeida , J. G. Pereira

In two-dimensional noncommutive space for the case of both position - position and momentum - momentum noncommuting, the consistent deformed bosonic algebra at the non-perturbation level described by the deformed annihilation and creation…

High Energy Physics - Theory · Physics 2009-07-10 Jian-Zu Zhang

We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity…

High Energy Physics - Theory · Physics 2015-05-13 Catarina Bastos , Orfeu Bertolami , Nuno Dias , Joao Nuno Prata

We show that a hypothesis that spacetime is quantum with coordinate algebra $[x^i,t]=\lambda_P x^i$, and spherical symmetry under rotations of the $x^i$, essentially requires in the classical limit that the spacetime metric is the…

General Relativity and Quantum Cosmology · Physics 2014-12-16 Shahn Majid , Wen-Qing Tao