Related papers: Construction of SO(5)>SO(3) spherical harmonics an…
This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic…
Representations of $SO(5)_{q}$ are constructed explicitly on the Chevalley basis for all $q$, generic and root of unity. Matrix elements of the generators are obtained for all representations depending on three variable indices, the maximal…
The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with…
A constructive procedure to obtain superintegrable deformations of the classical Smorodinsky-Winternitz Hamiltonian by using quantum deformations of its underlying Poisson sl(2) coalgebra symmetry is introduced. Through this example, the…
A closed SO(5) algebraic structure in the the mean-field form of the Hamiltonian the pure p-wave superconductivity is found that can help to diagonalized by making use of the Bogoliubov rotation instead of the Balian-Werthamer approach. we…
We prove a criterion of when a coaction of a compact Lie group on an algebra of continuous functions on a compact manifold extends to a coaction of deformation quantizations of the Lie group and the algebra. We compute an explicit example…
In this paper, we introduce C*-algebraic partial compact quantum groups, which are quantizations of topological groupoids with discrete object set and compact morphism spaces. These C*-algebraic partial compact quantum groups are…
Spherically symmetric solutions of the SU(5) Einstein-Yang-Mills-Higgs system are constructed using the harmonic map ansatz \cite{IS}. This way the problem reduces to solving a set of ordinary differential equations for the appropriate…
We construct finite Dyson boson-fermion mappings of general collective algebras extended by single-fermion operators. A key element in the construction is the implementation of a similarity transformation which transforms boson-fermion…
This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional…
The matrix elements of the quadrupole collective variables, emerging from collective nuclear models, are calculated in the natural Cartan-Weyl basis of O(5) which is a subgroup of a covering $SU(1,1)\times O(5)$ structure. Making use of an…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
A summary of the properties of the Wigner Clebsch-Gordan coefficients and isoscalar factors for the group SU3 in the SU2$\otimes$U1 decomposition is presented. The outer degeneracy problem is discussed in detail with a proof of a conjecture…
We calculate (q-deformed) Clebsch-Gordan and 6j-coefficients for rank two quantum groups. We explain in detail how such calculations are done, which should allow the reader to perform similar calculations in other cases. Moreover, we…
We study the role of symmetries in control systems through the geometric algebra approach. We discuss two specific control problems on Carnot groups of step $2$ invariant with respect to the action of $SO(3)$. We understand the geodesics as…
The unitary Clifford algebras are described here for the first time, and arise from the intersection of the orthogonal and common symplectic (Weyl) Clifford algebras of the complexification of the canonical phase space. The convergence of…
We present an operational reconstruction of the well-known two-to-one homomorphism between the groups $SU(2)$ and $SO(3)$, grounded in the physical description of quantum state preparation and evolution. Starting from the connection between…
In the Elliott SU(3) symmetry scheme the single particle basis is derived from the isotropic harmonic oscillator Hamiltonian in the Cartesian coordinate system. These states are transformed into the solutions of the same Hamiltonian within…
The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…