Related papers: SU(3) Richardson-Gaudin models: three level system…
We construct lists of supersymmetric models with extended gauge groups at intermediate steps, all of which are based on SO(10) unification. We consider three different kinds of setups: (i) The model has exactly one additional intermediate…
The elliptic Gaudin model describes completely anisotropic spin systems with long range interactions. The model was proven to be quantum integrable by Gaudin and latter the exact solution was found by means of the algebraic Bethe ansatz. In…
A type of prolongation structure for several general systems is discussed. They are based on a set of one-forms in which the underlying structure group of the integrability condition corresponds to the Lie-algebra of SL (2,R), O(3), or…
Quantum simulations of the dynamics of QCD have been limited by the complexities of mapping the continuous gauge fields onto quantum computers. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom, we…
The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum…
We generalize the SU(2|2) supersymmetric extended Hubbard model of 1/r2 interaction to the SU(m|n) supersymmetric case. Integrable models may be defined on both uniform lattice and non-uniform one dimensional lattices. We study both cases…
A microscopic interpretation of the s and d bosons of the Interacting Boson Model is being suggested: the s, d bosons can be interpreted as symmetric pairs of harmonic oscillator quanta of the valence nuclear shell. Within this…
In the first part we present the Weyl algebra and our results concerning its finite-dimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of…
A class of gauges for the Einstein vacuum equations is introduced, along with three symmetric hyperbolic systems. The first implies the local realizability of the gauge. The second is the dynamical subset of the field equations. The third…
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 differential operators, of the underlying Lie algebra. This is…
We develop a scheme to construct the Hamiltonians of the lambda, vee and cascade type of three-level configurations using the generators of SU(3) group. It turns out that this approach provides a well defined selection rule to give…
Elliott's SU(3) model is at the basis of the shell-model description of rotational motion in atomic nuclei. We demonstrate that SU(3) symmetry can be realized in a truncated shell-model space if constructed in terms of a sufficient number…
An extension of the Standard Model to the local gauge group $SU(3)_c\otimes SU(4)_L\otimes U(1)_X$ as a three-family model is presented. The model does not contain exotic electric charges and we obtain a consistent mass spectrum by…
We study a three dimensional analogue of the Wess--Zumino--Witten model, which describes the Goldstone bosons of three dimensional Quantum Chromodynamics. The topologically non--trivial term of the action can also be viewed as a nonlinear…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
We study the relation between the frame-like and metric-like formulation of higher-spin gauge theories in three space-time dimensions. We concentrate on the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the frame-like…
We compute the mass spectrum of the SU(2) adjoint Higgs model in 2+1 dimensions at several points located in the (metastable) confinement region of its phase diagram. We find a dense spectrum consisting of an almost unaltered repetition of…
We consider a Gaudin magnet (central spin model) with a time-dependent exchange couplings. We explicitly show that the Schr\"odinger equation is analytically solvable in terms of generalized hypergeometric functions for particular choices…
We consider the spectral and initial value problem for the Lindblad-Gorini-Kossakowski-Sudarshan master equation describing an open quantum system of bosons and spins, where the bosonic parts of the Hamiltonian and Lindblad jump operators…
In $~^3$He-B, two atoms pair in an orbital angular momentum $1$ spin triplet state above the phase transition temperature with $SO(3) \times SO(3)$ symmetry. Below the transition temperature, this symmetry is spontaneously broken to the…