73 citations · 638 across the 41 of their papers we have counts for
13 papers · 1 filter
Representations of the D=2 Euclidean and Poincaré groups
Giovanni Camilletti, María A. Lledó, Mariano A. del Olmo
We present an explicit construction of the unitary irreducible representations of the two-dimensional Euclidean and Poincaré groups, together with their Spin double covers, by mean…
Gelfand Triplets, Continuous and Discrete Bases and Legendre Polynomials
Enrico Celeghini, Manuel Gadella, Mariano A. del Olmo
We consider a basis of square integrable functions on a rectangle, contained in , constructed with Legendre polynomials, suitable, for instance, for the analogical description…
A Novel Holographic Framework Preserving Reflection Positivity in dS Spacetime
Jean-Pierre Gazeau, Mariano A. del Olmo, Hamed Pejhan
This manuscript introduces a novel holographic correspondence in -dimensional de Sitter (dS) spacetime, connecting bulk dS scalar unitary irreducible representations (UI…
Anti-de Sitterian "massive" elementary systems and their Minkowskian and Newton-Hooke contraction limits
Mohammad Enayati, Jean-Pierre Gazeau, Mariano A. del Olmo +1
We elaborate the definition and properties of "massive" elementary systems in the -dimensional Anti-de Sitter (AdS) spacetime, on both classical and quantum levels. We f…
Polynomial algebras from and the generic model on the two sphere
Francisco Correa, Mariano A. del Olmo, Ian Marquette +1
Construction of superintegrable systems based on Lie algebras have been introduced over the years. However, these approaches depend on explicit realisations, for instance as a diff…
Hermite functions and Fourier series
Enrico Celeghini, Manuel Gadella, Mariano. A. del Olmo
Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle () and in , which are related…
SU(2), Associated Laguerre Polynomials and Rigged Hilbert Spaces
Enrico Celeghini, Manuel Gadella, Mariano A. del Olmo
We present a family of unitary irreducible representations of SU(2) realized in the plane, in terms of the Laguerre polynomials. These functions are similar to the spherical harmon…
Quantum Physics and Signal Processing in Rigged Hilbert Spaces by means of Special Functions, Lie Algebras and Fourier and Fourier-like Transforms
Enrico Celeghini, Mariano A. del Olmo
Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variabl…
Lie Groups of Jacobi polynomials and Wigner d-matrices
E. Celeghini, M. A. del Olmo, M. A. Velasco
A symmetry group in terms of ladder operators is presented for the Jacobi polynomials, , and the Wigner -matrices where the spins int…
Jacobi polynomials and SU(2,2)
E. Celeghini, M. A. del Olmo, M. A. Velasco
A ladder structure of operators is presented for the Jacobi polynomials, J_n^(a,b)(x), with parameters n, a and b integers, showing that they are related to the unitary irreducible…
Algebraic special functions and so(3,2)
E. Celeghini, M. A. del Olmo
A ladder structure of operators is presented for the associated Legendre polynomials and the spherical harmonics showing that both belong to the same irreducible representation of…
Pisot q-Coherent states quantization of the harmonic oscillator
J. P. Gazeau, M. A. del Olmo
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0< q < 1, these normalized states form an overcomp…
Coherent Orthogonal Polynomials
E Celeghini, Mariano A del Olmo
We discuss as a fundamental characteristic of orthogonal polynomials like the existence of a Lie algebra behind them, can be added to their other relevant aspects. At the basis of…