222 citations · 1.6k across the 117 of their papers we have counts for
29 papers · 1 filter
Araki Cohomology of the de Sitter Scalar Discrete Series
Maryam Bajalan, Jean-Pierre Gazeau, Hamed Pejhan +1
Building on the recently established de Sitter (dS)-covariant indecomposable Krein realization of the scalar discrete-series unitary irreducible representations , $p=1,2,\…
Bi-Oriented Interlaced Matrix Multiplication and an Operator Factorisation of the Quantum Harmonic Oscillator
Jean-Pierre Gazeau
We introduce a bi-oriented interlaced matrix product on matrices over a unital, possibly non-associative algebra, extending a matrix mnemonic for Cayley--Dickson doubli…
de Sitter Scalar Discrete Series: Gupta-Bleuler Structure and Holography
Maryam Bajalan, Jean-Pierre Gazeau, Hamed Pejhan
We show that scalar discrete-series unitary irreducible representations (UIRs) () of the de Sitter (dS) group admit a dS-covariant Krei…
Massless Representations in Conformal Space and Their de Sitter Restrictions
Jean-Pierre Gazeau, Hamed Pejhan, Ivan Todorov
The monograph offers a coherent and self-contained treatment of massless (ladder) representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2)…
Matrix Elements and Characters of the Discrete Series ("Massive") Unitary Irreducible Representations of Sp(4,R)
Jean-Pierre Gazeau, Mariano A. del Olmo, Hamed Pejhan
This paper obtains the matrix elements and characters of the discrete series unitary irreducible representations (UIRs) of the Sp group. With an isomorphic relation…
Regularized quantum motion in a bounded set: Hilbertian aspects
Fabio Bagarello, Jean-Pierre Gazeau, Camillo Trapani
It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditio…
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…
The de Sitter group and its representations: a window on the notion of de Sitterian elementary systems
Mohammad Enayati, Jean-Pierre Gazeau, Hamed Pejhan +1
We review the construction of ("free") elementary systems in de Sitter (dS) spacetime, in the Wigner sense, as associated with unitary irreducible representations (UIR's) of the dS…
2-D Covariant Affine Integral Quantization(s)
Jean Pierre Gazeau, Tomoi Koide, Romain Murenzi
Covariant affine integral quantization is studied and applied to the motion of a particle in a punctured plane R^2_\ast=R^2\{0}, for which the phase space is R^2_\ast=R^2\{0}X R^2.…
Covariant integral quantization of the unit disk
Mariano A. del Olmo, Jean Pierre Gazeau
We implement a SU(1,1) covariant integral quantization of functions or distributions on the unit disk. The latter can be viewed as the phase space for the motion of a test "massive…
Generalized Heisenberg algebra and (non linear) pseudo-bosons
Fabio Bagarello, Evaldo M. F. Curado, Jean-Pierre Gazeau
We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non…
Quantum localisation on the circle
Rodrigo Fresneda, Jean Pierre Gazeau, Diego Noguera
Covariant integral quantisation using coherent states for semidirect product groups is studied and applied to the motion of a particle on the circle. In the present case the group…
-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization
S. Twareque Ali, Fabio Bagarello, Jean Pierre Gazeau
The -pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible r…
Extended pseudo-fermions from non commutative bosons
Syed Twareque Ali, Fabio Bagarello, Jean Pierre Gazeau
We consider some modifications of the two dimensional canonical commutation relations, leading to {\em non commutative bosons} and we show how biorthogonal bases of the Hilbert spa…
Symmetric generalized binomial distributions
H. Bergeron, E. M. F. Curado, J. P. Gazeau +1
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilit…
Quantizations from reproducing kernel spaces
S. Twareque Ali, Fabio Bagarello, Jean Pierre Gazeau
The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of $L^2(\C, \, d^2z/π)$ based on subsets of complex Hermite polynomials.…
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…
Generating functions for generalized binomial distributions
H. Bergeron, E. M. F. Curado, J. P. Gazeau +1
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal exp…
On a generalization of the binomial distribution and its Poisson-like limit
E. M. F. Curado, J. P. Gazeau, Ligia M. C. S. Rodrigues
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might b…
Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons
Syed Twareque Ali, Fabio Bagarello, Jean-Pierre Gazeau
In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canon…
Coherent States and Bayesian Duality
S. Twareque Ali, J. -P. Gazeau, B. Heller
We demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of a reproducing kernel Hilbert sp…
Finite tight frames and some applications
Nicolae Cotfas, Jean Pierre Gazeau
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete…
Asymptotic behavior of beta-integers
L. Balková, J. P. Gazeau, E. Pelantová
Beta-integers (``-integers'') are those numbers which are the counterparts of integers when real numbers are expressed in irrational basis . In quasicrystalline studies $β…