Related papers: Connection between Elliott SU(3) and spherical she…
The Standard Model of the theory of elementary particles is based on the $U(1)\times SU(2)\times SU(3)$ symmetry. In the presence of a gravitation field, i. e. in a non-flat space-time manifold, this symmetry is implemented through three…
For SU(2) gauge theory on the three-sphere we implement the influence of the boundary of the fundamental domain, and in particular the $\theta$-dependence, on a subspace of low-energy modes of the gauge field. We construct a basis of…
Spin-orbit coupling in crystals is known to lead to unusual direction dependent exchange interactions, however understanding of the consequeces of such effects in molecular crystals is incomplete. Here we perform four component relativistic…
The su(1$|$1) symmetric version of the Haldane-Shastry spin chain is diagonalized by means of a linear transformation. The same transformation applied to the original su(2) model yields simple expressions for the Hamiltonian and the…
We construct the singlet Hilbert space associated with addition of SU(3) generators. This corresponds to the solution of Gauss law in lattice QCD. The normalized basis states are explicitly constructed using Schwinger Bosons. Further, we…
A symmetry-based approach for describing shape-coexistence, is presented in the framework of the interacting boson model of nuclei. It involves a construction of a number-conserving Hamiltonian which preserves the dynamical symmetry of…
We consider $\mathbb{R}^3$ as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary $\tau\in \widehat{SO(3)}$, let $E_\tau$ be the homogeneous vector bundle over $\mathbb{R}^3$…
The optically induced oscillatory response of a spherical two-component, shell-core structured, nanoparticle by nodeless elastic vibrations of soft peripheral shell against hard and dynamically immobile inner core is considered. The…
We perform Monte Carlo simulations of a three-dimensional spin system with a Hamiltonian which contains only four-spin interaction term. This system describes random surfaces with extrinsic curvature - gonihedric action. We study the…
We investigate some properties of the standard rotator approximation of the SU$(N)\times\,$SU$(N)$ sigma-model in the delta-regime. In particular we show that the isospin susceptibility calculated in this framework agrees with that computed…
The general solution of SUSY intertwining relations for three-dimensional Schr\"odinger operators is built using the class of second order supercharges with nondegenerate constant metric. This solution includes several models with arbitrary…
Exact diagonalization and other numerical studies of quantum spin systems are notoriously limited by the exponential growth of the Hilbert space dimension with system size. A common and well-known practice to reduce this increasing…
We develop a multi-reference perturbation theory for electronic structure calculations based on symmetries of the Hamiltonian. The reference Hamiltonian in the symmetry-based perturbation theory (SBPT) is chosen such that it possesses more…
To study circularly symmetric field configurations in the SU(2) Hitchin system an SO(2) symmetry, [J_3, \phi]=0 and [J_3, A_{\pm}]=\pm A_{\pm}, is imposed on the Higgs scalar \phi and the gauge fields A_{\pm} of the system, respectively,…
We develop uniform approximations for the trace formula for non-integrable systems in which SU(2) symmetry is broken by a non-linear term of the Hamiltonian. As specific examples, we investigate H\'enon-Heiles type potentials. Our formalism…
Recently, Hirayama and Yamashita have presented an ansatz that allows us to construct a class of solutions for the SU(2) Skyrme model. Though these solutions are not solitonic, they provide us with an example on how the plane wave solutions…
We construct a three-dimensional superconformal quantum mechanics (and its associated de Alfaro-Fubini-Furlan deformed oscillator) possessing an $sl(2|1)$ dynamical symmetry. At a coupling parameter $\beta\neq 0$ the Hamiltonian contains a…
The non-equilibrium dynamics of quantum spin models is a most challenging topic, due to the exponentiality of Hilbert space; and it is central to the understanding of the many-body entangled states that can be generated by state-of-the-art…
Following the basic idea developed in (I), the su(3)-model presented by Elliott is investigated. A method for constructing the orthogonal set, in which the angular momenta are good quantum numbers, is discussed without using the angular…
This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian…