scholarly journals Interplay between Spacetime Curvature, Speed of Light and Quantum Deformations of Relativistic Symmetries

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2099
Author(s):  
Angel Ballesteros ◽  
Giulia Gubitosi ◽  
Flavio Mercati
Keyword(s):  
Deformation Parameter ◽  
Planck Scale ◽  
Quantum Deformation ◽  
Speed Of Light ◽  
Spacetime Curvature ◽  
Quantum Gravity Phenomenology ◽  
Poincaré Algebra ◽  
Quantum Deformations ◽  
Curvature Parameter ◽  
Relativistic Models

Recent work showed that κ-deformations can describe the quantum deformation of several relativistic models that have been proposed in the context of quantum gravity phenomenology. Starting from the Poincaré algebra of special-relativistic symmetries, one can toggle the curvature parameter Λ, the Planck scale quantum deformation parameter κ and the speed of light parameter c to move to the well-studied κ-Poincaré algebra, the (quantum) (A)dS algebra, the (quantum) Galilei and Carroll algebras and their curved versions. In this review, we survey the properties and relations of these algebras of relativistic symmetries and their associated noncommutative spacetimes, emphasizing the nontrivial effects of interplay between curvature, quantum deformation and speed of light parameters.

scholarly journals Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Ángel Ballesteros ◽  
N. Rossano Bruno ◽  
Francisco J. Herranz
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Lie Algebras ◽  
Deformation Parameter ◽  
Planck Scale ◽  
Quantum Deformation ◽  
De Sitter ◽  
Planck Length ◽  
Unified Approach ◽  
Drinfel’D Double

Theκ-deformation of the (2 + 1)D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel’d-double and the Poisson–Lie structure underlying theκ-deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson–Lie algebras. As a consequence, the noncommutative (2 + 1)D spacetimes that generalize theκ-Minkowski space to the (anti-)de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like) geodesics can be defined, and they can be interpreted as a novel possibility to introduce noncommutative worldlines. Furthermore, quantum (anti-)de Sitter algebras are presented both in the known basis related to 2 + 1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related to the Planck length, and the existence of a kind of “duality” between the cosmological constant and the Planck scale is also envisaged.

scholarly journals Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1309
Author(s):  
Jerzy Lukierski
Keyword(s):  
Phase Space ◽  
Hopf Algebras ◽  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Planck Length ◽  
Covariant Quantum ◽  
Drinfeld Twist ◽  
Quantum Deformations ◽  
Heisenberg Double ◽  
Conformal Symmetries

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

Five-dimensional Brans–Dicke compactified universe dominated by a varying speed of light

2020 ◽  
Vol 35 (30) ◽  
pp. 2050252
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
Killing Vector ◽  
Scalar Fields ◽  
Analytic Solutions ◽  
Accelerated Expansion ◽  
Late Time ◽  
Speed Of Light ◽  
Orthogonal Space ◽  
Spacetime Curvature ◽  
The Universe ◽  
Data Analytic

We extend the model of a 5D Brans–Dicke gravity theory reduced to 4D through the presence of a hypersurface-orthogonal space-like killing vector field in the underlying 5D spacetime by including a varying speed of light. The resulting model is characterized by the presence of two scalar fields. We focus on late-time power law solutions which emerge in general when scalar fields couple to spacetime curvature and do not contradict the SNIa astrophysical data. Analytic solutions in 4-dimensions are derived and late-time accelerated expansion was found. The universe is dominated by dark energy, free from phantom field and is characterized by a decaying energy matter density, decaying scalar fields, and a decreasing celerity of light. The model is confronted with astrophysical observations and is found to fit these data.

scholarly journals THE CLASSICAL BASIS FOR κ-DEFORMED POINCARÉ ALGEBRA AND SUPERALGEBRA

1995 ◽  
Vol 10 (34) ◽  
pp. 2599-2606 ◽  
Author(s):  
P. KOSIŃSKI ◽  
J. LUKIERSKI ◽  
J. SOBCZYK ◽  
P. MAŚLANKA
Keyword(s):  
General Solution ◽  
Quantum Deformation ◽  
Poincaré Algebra

We describe here the general solution describing generators of κ-deformed Poincaré algebra as the functions of classical Poincaré algebra generators as well as the inverse formulas. Further we present analogous relations for the generators of N=1, D=4 κ-deformed Poincaré superalgebra expressed by the classical Poincaré superalgebra generators. In such a way we obtain the κ-deformed Poincaré (super)algebras with all the quantum deformation present only in the co-algebra sector. As an application we use the classical basis of κ-deformed Poincaré superalgebra for obtaining a new result: the κ-deformation of supersymmetric spin (Pauli-Lubanski) Casimir.

scholarly journals MOND and natural scales of distance and mass

2019 ◽  
Vol 34 (37) ◽  
pp. 1950306
Author(s):  
Piotr Żenczykowski
Keyword(s):  
Gravitational Constant ◽  
Planck Scale ◽  
General Nature ◽  
Nanometer Scale ◽  
Physical Interaction ◽  
Speed Of Light ◽  
Planck Constant ◽  
System Of Units ◽  
Related Approach ◽  
The Universe

We describe a MOND-related approach to natural scales of distance and mass, viewing it as a logical step following Planck’s modification of the Stoney system of units. The MOND-induced scales are not based on the strength of any physical interaction (electromagnetic, gravitational, or otherwise). Instead, they are specified by three physical constants of a general nature that define the scales of action, speed, and acceleration, i.e. [Formula: see text] — the Planck constant, [Formula: see text] — the speed of light and [Formula: see text] — the MOND acceleration constant. When the gravitational constant [Formula: see text] is added, two further distance scales (apart from the size of the Universe) appear: the Planck scale and a nanometer scale that fits the typical borderline between the classical and the quantum descriptions.

Gravitational waves, energy and Feynman’s “sticky bead”

2015 ◽  
Vol 30 (27) ◽  
pp. 1550143 ◽  
Author(s):  
F. I. Cooperstock
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Electromagnetic Waves ◽  
Vacuum Energy ◽  
Cosmological Term ◽  
Speed Of Light ◽  
Field Equations ◽  
Energy Expression ◽  
Energy Issue ◽  
Spacetime Curvature

It is noted that in the broader sense, gravitational waves viewed as spacetime curvature which necessarily accompanies electromagnetic waves at the speed of light, are the routine perception of our everyday experience. We focus on the energy issue and Feynman’s “sticky bead” argument which has been regarded as central in supporting the conclusion that gravitational waves carry energy through the vacuum in general relativity. We discuss the essential neglected aspects of his approach which leads to the conclusion that gravitational waves would not cause Feynman’s bead to heat the stick on which it would supposedly rub. This opens the way to an examination of the entire issue of energy in general relativity. We briefly discuss our naturally-defined totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity. When the cosmological term is included in the field equations, our energy expression includes the vacuum energy as required.

Non-commutative quantum gravity phenomenology in underground experiments

2019 ◽  
Vol 34 (29) ◽  
pp. 1950236 ◽  
Author(s):  
Andrea Addazi ◽  
Rita Bernabei
Keyword(s):  
Laboratory Experiments ◽  
Planck Scale ◽  
Pauli Exclusion Principle ◽  
Energy Scale ◽  
Exclusion Principle ◽  
Atomic Systems ◽  
Quantum Gravity Phenomenology ◽  
Nuclear Transitions ◽  
Moyal Plane ◽  
Very High

We show how non-commutative spacetime models can induce Pauli Exclusion Principle (PEP) forbidden nuclear and atomic transitions. We focalize our analysis on one of the most popular instantiations of non-commutativeness: [Formula: see text]-Poincaré model, based on the Groenewold–Moyal plane algebra. We show that PEP violating transitions induced by [Formula: see text]-Poincaré have an energy scale and angular emission dependence. PEP violating transitions in nuclear and atomic systems can be tested with very high accuracy in underground laboratory experiments such as DAMA/LIBRA and VIP(2). We derive that the Equivalence Principle assumed [Formula: see text]-Poincaré model can be already ruled-out until the Planck scale, from nuclear transitions tests by DAMA/LIBRA experiment.

scholarly journals Generalized Dirac oscillator with κ-Poincaré algebra

2020 ◽  
Vol 29 (05) ◽  
pp. 2050033
Author(s):  
Jing Wu ◽  
Chao-Yun Long ◽  
Zheng-Xue Wu ◽  
Zheng-Wen Long
Keyword(s):  
Deformation Parameter ◽  
Singular Potential ◽  
Dimensional Space ◽  
Energy Levels ◽  
Quantum Systems ◽  
Energy Spectra ◽  
Dirac Oscillator ◽  
Radial Equation ◽  
Poincaré Algebra ◽  
Type Potential

In this paper, the generalized Dirac oscillator with [Formula: see text]-Poincaré algebra is structured by replacing the momentum operator p with [Formula: see text] in [Formula: see text]-deformation Dirac equation. The deformed radial equation is derived for this model. Particularly, by solving the deformed radial equation, the wave functions and energy spectra which depend on deformation parameter [Formula: see text] have been obtained for these quantum systems with [Formula: see text] being a Yukawa-type potential, inverse-square-type singular potential and central fraction power singular potential in two-dimensional space, respectively. The results show that the deformation parameter [Formula: see text] can lead to decreasing of energy levels for the above quantum systems. At the same time, the degeneracy of energy spectra has been discussed and the corresponding conditions of degeneracy have been given for each case.

scholarly journals Q-DEFORMED OSCILLATOR ALGEBRA AND AN INDEX THEOREM FOR THE PHOTON PHASE OPERATOR

1995 ◽  
Vol 10 (33) ◽  
pp. 2543-2551 ◽  
Author(s):  
KAZUO FUJIKAWA ◽  
L.C. KWEK ◽  
C.H. OH
Keyword(s):  
Deformation Parameter ◽  
Matrix Representation ◽  
Index Theorem ◽  
Oscillator Algebra ◽  
Quantum Deformation ◽  
Phase Operator ◽  
Negative Norm ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra ◽  
Index Condition

The quantum deformation of the oscillator algebra and its implications on the phase operator are studied from a viewpoint of an index theorem by using an explicit matrix representation. For a positive deformation parameter q or q=exp(2πiθ) with an irrational θ, one obtains an index condition dim ker a–dim ker a†=1 which allows only a nonhermitian phase operator with dim ker eiφ–dim ker(eiφ)†=1. For q=exp(2πiθ) with a rational θ, one formally obtains the singular situation dim ker a=∞ and dim ker a†=∞, which allows a hermitian phase operator with dim ker eiΦ–dim ker(eiΦ)†=0 as well as the nonhermitian one with dim ker eiφ– dim ker(eiφ)†=1. Implications of this interpretation of the quantum deformation are discussed. We also show how to overcome the problem of negative norm for q=exp(2πiθ).

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