© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:nucl-th/9512017 · Romanian Journal of Physics

Quantum Algebras in Nuclear Structure

Dennis Bonatsos A, C. Daskaloyannis, P. Kolokotronis, D. Lenis

Published Dec 12, 1995• 5 citations

Abstract

Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools ($q$-numbers, $q$-analysis, $q$-oscillators, $q$-algebras), the su$_q$(2) rotator model and its extensions, the construction of deformed exactly soluble models (Interacting Boson Model, Moszkowski model), the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to molecular structure and an outlook are also given.

DOI: 10.48550/arxiv.nucl-th/9512017

Related papers

Quantum algebraic symmetries in atomic nuclei and metal clusters

Dennis Bonatsos A, B. A. Kotso, P. Raychev +1 more

Using irreducible tensor operators under su q (2) a rotationally invariant Hamiltonian which provides a good description of nuclear rotational spectra is constructed and its relation to existing nuclear models is considered. Using the same techniques a 3dimensional g-deformed harmonic oscillator with u q (3)⊃so q (3) symmetry is constructed, compared to the modified oscillator of Nilsson, and used for the successful description of magic numbers and supershells in metal clusters.

CRC Press eBooks•Nov 30, 2003•0 citations

Multidimensional isotropic and anisotropicq-oscillator models

A Ghosh, P Mitra, A Kundu

q-oscillator models are considered in two and higher dimensions and their symmetries are explored. New symmetries are found for both isotropic and anisotropic cases. Applications to the spectra of triatomic molecules and superdeformed nuclei are discussed.

arXiv:hep-th/9511084•Journal of Physics A Mathematical and General•Jan 7, 1996•3 citations

Quantum algebraic symmetries in nuclear physics

Dennis Bonatsos A, C. Dascaloyannis

The pairing correlations in a single-j nuclear shell are considered. It is proven that a simple boson mapping in terms of q-defonned bosons exists, which reproduces correctly both the commutation relations and the energy up to first order corrections, the parameter q being connected to the size of the shell. An exact solution in terms of a generalized deformed oscillator is also found

HNPS Advances in Nuclear Physics•Dec 5, 2019•0 citations

The Universal Algebraic Structure of Exactly Solvable Quantum Systems

Revista, Zen, PHYSICS, 10

Exactly solvable quantum systems represent a fascinating and critically important class of models in theoretical physics, offering exact solutions to non-trivial problems that often shed light on the behavior of more complex, intractable systems. The remarkable feature of these systems lies not only in their solvability but also in the underlying mathematical structures that facilitate such solutions. This paper explores the concept of a universal algebraic structure that underpins exactly solvable quantum systems. We delve into how diverse models, ranging from one-dimensional spin chains to many-body systems and field theories, exhibit common algebraic symmetries, such as Lie algebras, affine Lie algebras, and quantum groups. These algebraic frameworks provide a unified language for understanding integrability, the existence of an infinite number of conserved quantities, and the ability to construct exact eigenstates. We review the historical development of these ideas, from the Bethe ansatz to the development of the inverse scattering method and quantum groups. Our discussion highlights how these mathematical structures are not merely tools for calculation but fundamental descriptors of the physical reality of these systems, offering profound insights into non-perturbative quantum phenomena. The identification of a universal algebraic architecture suggests a deeper coherence in the landscape of quantum mechanics, paving the way for new discoveries and classifications of quantum models.

•Nov 28, 2025•0 citations

Fermion-boson interactions and quantum algebras

Ángel Ballesteros, Osvaldo Civitarese, Francisco J. Herranz +1 more

Quantum algebras $(q$ algebras) are used to describe interactions between fermions and bosons. Particularly, the concept of a ${\mathrm{su}}_{q}(2)$ dynamical symmetry is invoked in order to reproduce the ground state properties of systems of fermions and bosons interacting via schematic forces. The structure of the proposed ${\mathrm{su}}_{q}(2)$ Hamiltonians, and the meaning of the corresponding deformation parameters, are discussed.

arXiv:nucl-th/0212022•Physical Review C•Dec 30, 2002•42 citations

Quantum Mechanics for Nuclear Structure, Volume 1

K. Heyde

Quantum Mechanics for Nuclear Structure, Volume two follows on from its predecessor by examining topics essential for understanding the many-body formulation. The algebraic structure of quantum theory is emphasised throughout as an essential aspect of the mathematical formulation of many-body quantum systems.

•Dec 3, 2019•0 citations

Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools (

q

-numbers,

q

-analysis,

q

-oscillators,

q

-algebras), the su

_q

(2) rotator model and its extensions, the construction of deformed exactly soluble models (Interacting Boson Model, Moszkowski model), the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to molecular structure and an outlook are also given.

Exactly solvable quantum systems represent a fascinating and critically important class of models in theoretical physics, offering exact solutions to non-trivial problems that often shed light on the behavior of more complex, intractable systems. The remarkable feature of these systems lies not only in their solvability but also in the underlying mathematical structures that facilitate such solutions. This paper explores the concept of a universal algebraic structure that underpins exactly solvable quantum systems. We delve into how diverse models, ranging from one-dimensional spin chains to many-body systems and field theories, exhibit common algebraic symmetries, such as Lie algebras, affine Lie algebras, and quantum groups. These algebraic frameworks provide a unified language for understanding integrability, the existence of an infinite number of conserved quantities, and the ability to construct exact eigenstates. We review the historical development of these ideas, from the Bethe ansatz to the development of the inverse scattering method and quantum groups. Our discussion highlights how these mathematical structures are not merely tools for calculation but fundamental descriptors of the physical reality of these systems, offering profound insights into non-perturbative quantum phenomena. The identification of a universal algebraic architecture suggests a deeper coherence in the landscape of quantum mechanics, paving the way for new discoveries and classifications of quantum models.

Quantum algebras

(q

algebras) are used to describe interactions between fermions and bosons. Particularly, the concept of a

{\mathrm{su}}_{q}(2)

dynamical symmetry is invoked in order to reproduce the ground state properties of systems of fermions and bosons interacting via schematic forces. The structure of the proposed

{\mathrm{su}}_{q}(2)

Hamiltonians, and the meaning of the corresponding deformation parameters, are discussed.