A5001226381- Nonlinear Waves and Solitons
- Algebraic structures and combinatorial models
- Advanced Topics in Algebra
- Quantum Mechanics and Non-Hermitian Physics
- Noncommutative and Quantum Gravity Theories
- Black Holes and Theoretical Physics
- Homotopy and Cohomology in Algebraic Topology
- Quantum chaos and dynamical systems
- Advanced Differential Geometry Research
- Molecular spectroscopy and chirality
- Nonlinear Photonic Systems
- Advanced Operator Algebra Research
- Advanced Algebra and Geometry
- Advanced Fiber Laser Technologies
- Cosmology and Gravitation Theories
- Algebraic and Geometric Analysis
- Mathematics and Applications
- Quantum Information and Cryptography
- Geometric and Algebraic Topology
- Protein Structure and Dynamics
- Cold Atom Physics and Bose-Einstein Condensates
- Relativity and Gravitational Theory
- Optical Network Technologies
- Quantum, superfluid, helium dynamics
- Sphingolipid Metabolism and Signaling
Universidad de Burgos
2015-2024
Universidad Complutense de Madrid
2023
Universidad de Valladolid
1993-1997
The exploration of the universe has recently entered a new era thanks to multi-messenger paradigm, characterized by continuous increase in quantity and quality experimental data that is obtained detection various cosmic messengers (photons, neutrinos, rays gravitational waves) from numerous origins. They give us information about their sources properties intergalactic medium. Moreover, astronomy opens up possibility search for phenomenological signatures quantum gravity. On one hand, most...
Abstract We show that the Lorentzian Snyder models, together with their Galilei and Carroll limiting cases, can be rigorously constructed through projective geometry description of Lorentzian, Galilean Carrollian spaces nonvanishing constant curvature. The coordinates such curved take role momenta, while translation generators over same are identified noncommutative spacetime coordinates. In this way, one obtains a deformed phase space algebra, which fully characterizes model is invariant...
A simultaneous and global scheme of quantum deformation is defined for the set algebras corresponding to groups motions two-dimensional Cayley-Klein geometries. Their central extensions are also considered under this unified pattern. In both cases some fundamental properties characterizing classical CK geometries (as existence a commuting involutions, contractions dualities relationships), remain in version.
The superposition of the Kepler–Coulomb potential on 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable (Verrier and Evans 2008 J. Math. Phys. 49 022902) by finding an additional (hidden) integral motion which is quartic in momenta. In this paper, we present generalization result N-dimensional spherical, hyperbolic spaces making use a unified symmetry approach that makes curvature parameter. resulting Hamiltonian, formed (curved) together...
The (3+1)-dimensional κ-(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which the Poisson homogeneous space. This turns out to be only possible generalization of well-known κ-Minkowski case non-vanishing cosmological constant, under condition that time translation generator corresponding quantum (A)dS algebra primitive. Moreover, shown have a quadratic subalgebra local spatial coordinates whose first-order brackets in terms constant...
A new method to obtain trigonometry for the real spaces of constant curvature and metric any (even degenerate) signature is presented. The could be described as `curvature/signature (in)dependent trigonometry' encapsulates all these into a single basic trigonometric group equation. This brings its logical end idea an `absolute trigonometry', provides equations which hold true nine two-dimensional signature. family includes both relativistic non-relativistic spacetimes; therefore complete...
An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set (2N − 3) functionally independent constants motion. Among them, two different subsets N integrals in involution (including Hamiltonian) can always be explicitly identified. As particular cases, we recover straightforward way most superintegrability properties Smorodinsky–Winternitz generalized Kepler–Coulomb systems constant...
In this paper, we give a unified and global new approach to the study of conformal structure three classical Riemannian spaces as well six relativistic non-relativistic spacetimes (Minkowskian, de Sitter, anti-de both Newton–Hooke Galilean). We obtain general expressions within Cayley–Klein framework, holding simultaneously for all these nine spaces, whose cycles (including geodesics circles) are explicitly characterized in way. The corresponding cycle-preserving symmetries, which rise...
The quantum duality principle is used to obtain explicitly the Poisson analogue of kappa-(A)dS algebra in (3+1) dimensions as corresponding Poisson-Lie structure on dual solvable Lie group. construction fully performed a kinematical basis and deformed Casimir functions are also obtained. cosmological constant $\Lambda$ included group contraction parameter, limit $\Lambda\to 0$ leads well-known kappa-Poincar\'e bicrossproduct basis. A twisted version with Drinfel'd double this deformation sketched.
An integrable generalization on the 2D sphere S2 and hyperbolic plane H2 of Euclidean anisotropic oscillator Hamiltonian with 'centrifugal' terms given by is presented. The resulting generalized depends explicitly constant Gaussian curvature κ underlying space, in such a way that all results here presented hold simultaneously for (κ > 0), < 0) E2 = 0). Moreover, shown to be any values parameters δ, Ω, λ1 λ2. Therefore, can also interpreted as an curved Higgs oscillator, recovered isotropic...
A Lie-Hamilton system is a nonautonomous of first-order ordinary differential equations describing the integral curves $t$-dependent vector field taking values in finite-dimensional real Lie algebra Hamiltonian fields with respect to Poisson structure. We provide new algebraic/geometric techniques easily determine properties such algebras on plane, e.g., their associated bivectors. study and known systems $\mathbb{R}^2$ physical, biological mathematical applications. New results cover...
We consider the quantum analog of generalized Zernike systems given by Hamiltonian: $$ \hat{\mathcal{H}} _N =\hat{p}_1^2+\hat{p}_2^2+\sum_{k=1}^N \gamma_k (\hat{q}_1 \hat{p}_1+\hat{q}_2 \hat{p}_2)^k , with canonical operators $\hat{q}_i,\, \hat{p}_i$ and arbitrary coefficients $\gamma_k$. This two-dimensional model, besides conservation angular momentum, exhibits higher-order integrals motion within enveloping algebra Heisenberg $\mathfrak h_2$. By constructing suitable combinations these...
We propose an adaptation of the notion scaling symmetries for case Lie-Hamilton systems, allowing their subsequent reduction to contact Lie systems. As illustration procedure, time-dependent frequency oscillators and thermodynamic systems are analyzed from this point view. The formalism provides a novel method constructing on three-dimensional sphere, derived recently established arising fundamental four-dimensional representation symplectic algebra $\mathfrak{sp}(4,\mathbb{R})$. It is shown...
A unified algebraic construction of the classical Smorodinsky–Winternitz systems on ND sphere, Euclidean and hyperbolic spaces through Lie groups SO(N + 1), ISO(N) SO(N, 1) is presented. Firstly, general expressions for Hamiltonian its integrals motion are given in a linear ambient space N+1, secondly they expressed terms two geodesic coordinate themselves, with an explicit dependence curvature as parameter. On potential interpreted superposition N 1 oscillators. Furthermore, each algebra...
A global model of the q deformation for quasiorthogonal Lie algebras generating groups motions four-dimensional affine Cayley–Klein (CK) geometries is obtained starting from three-dimensional deformations. It shown how main algebraic classical properties CK systems can be implemented in quantum case. Quantum deformed versions either space–time or space symmetry [Poincaré (3+1), Galilei 4-D Euclidean as well others] appear this context particular cases. For some these several deformations are...
In this paper we give an approach to quantum deformations of the (2+1) kinematical Lie algebras within a scheme that simultaneously describes all groups motions classical geometries in N=3 dimensions. We cover at once including versions Inonu-Wigner contractions, which are defined natural way and relate q-deformations as expected. thus obtain some previously known for three-dimensional Euclidean (2+1)-Poincare also new these other algebras, such (2+1)-de Sitter, Galilei Newton-Hooke algebras.
The coalgebra approach to the construction of classical integrable systems from Poisson coalgebras is reviewed, and essential role played by symplectic realizations in this framework emphasized. Many examples Hamiltonians with either undeformed or q-deformed symmetry are given, their Liouville superintegrability discussed. Among them, (quasi-maximally) superintegrable on N-dimensional curved spaces nonconstant curvature analysed detail. Further generalizations that make use comodule loop...
All possible Drinfel'd double structures for the anti-de Sitter Lie algebra so(2, 2) and de so(3, 1) in (2+1)-dimensions are explicitly constructed analysed terms of a kinematical basis adapted to (2+1)-gravity.Each these provides canonical way pairing among (anti-)de generators, as well specific classical r-matrix, cosmological constant is included them deformation parameter.It shown that four give rise structure Poincaré iso(2, limit where tends zero.We explain how (2+1)gravity, we show...
Curved momentum spaces associated to the $\ensuremath{\kappa}$-deformation of ($3+1$) de Sitter and anti--de algebras are constructed as orbits suitable actions dual Poisson-Lie group with nonvanishing cosmological constant. The $\ensuremath{\kappa}$-de $\ensuremath{\kappa}$-anti--de curved separately analyzed, they turn out be, respectively, half ($6+1$)-dimensional space a $\mathrm{SO}(4,4)$ invariance. Such made momenta spacetime translations ``hyperbolic'' boost transformations. known...