Related papers: Automated calculation of spin, isospin branching r…
A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group-subgroup chains is presented. The canonical U(4)->U(3)->U(2)->U(1) coupling and recoupling coefficients are applicable to…
A century ago, Wigner's SU(4) symmetry was introduced to explain the properties of atomic nuclei. Despite recent revived interest, its impact on nuclear structure, transitions, and reactions has not been fully explored. Here, we show that a…
We present the new version of the Mathematica package SARAH which provides the same features for a non-supersymmetric model as previous versions for supersymmetric models. This includes an easy and straightforward definition of the model,…
An exactly solvable sp(4) algebraic approach extends beyond the traditional isospin conserving nuclear interaction to bring forward effects of isospin symmetry breaking and isospin mixing resulting from a two-body nuclear interaction that…
We study theories of 4D, N=1 supersymmetric massless, arbitrary integer superspins. A new state-of-the art is being established by the discovery of a new series of such theories for arbitrary superspin Y (Y=s for any integer s) The lowest…
The relativistic mean field theory in combination with the analytic continuation in the coupling constant method is used to determine the energies and widths of single-particle resonant states in Sn isotopes. It is shown that there exists…
The SU(3) irreducible representations (irreps) are characterised by the (lambda, mu) Elliott quantum numbers, which are necessary for the extraction of the nuclear deformation, the energy spectrum and the transition probabilities. These…
We present a systematic method to classify the four-level system using $SU(4)$ symmetry as the basis group. It is shown that this symmetry allows three dipole transitions which eventually leads to six possible configurations of the…
We show that nuclear interactions are SU(4) symmetric at leading order in chiral perturbation theory in the large-N limit of QCD. The nucleons and delta resonances form a 20-dimensional representation of SU(4) and we show how Wigner's…
Spin network technique is usually generalized to relativistic case by changing $SO(4)$ group -- Euclidean counterpart of the Lorentz group -- to its universal spin covering $SU(2)\times SU(2)$, or by using the representations of $SO(3,1)$…
Bases for SU(3) irreps are constructed on a space of three-particle tensor products of two-dimensional harmonic oscillator wave functions. The Weyl group is represented as the symmetric group of permutations of the particle coordinates of…
We perform a systematic study of $SU(2)$ flavor amplitude sum rules with particular emphasis on $U$-spin. This study reveals a rich mathematical structure underlying the sum rules that allows us to formulate an algorithm for deriving all…
A countable set of superintegrable quantum mechanical systems is presented which admit the dynamical symmetry with respect to algebra so(4). This algebra is generated by the Laplace-Runge-Lenz vector generalized to the case of arbitrary…
A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group-subgroup chains is presented. While the canonical U(3)->U(2)->U(1) coupling and recoupling coefficients are applicable to any…
Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the…
We present the program SuSpect3 that calculates the masses and couplings of the Higgs and supersymmetric particles predicted by the Minimal Supersymmetric Standard Model (MSSM). The model is implemented in both its non-constrained version,…
We present an algorithmic classification of the irreps of the $N$-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields. Our work is based on the 1-to-1 \cite{pt} correspondence between Weyl-type…
We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…
We show how to include in the existing calculations for nuclei other than $^{129}$Xe, $^{131}$Xe, the corrections to the isovector coupling arising in chiral effective field theory recently found in Ref. \cite{Menendez1}. The dominant,…