https://archive-ouverte.unige.ch/unige:115288/ATTACHMENT01

Bicrossproduct structure of κ-Poincare group and non-commutative geometry

We show that the $\kappa$-deformed Poincar\'e quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct $U(so(1,3))\cobicross T$. The algebra is a semidirect product of the classical Lorentz group $so(1,3)$ acting in a deformed way on the momentum sector $T$. The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the $\kappa$-Poincar\'e acts covariantly on a $\kappa$-Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics.

/pdf/bicrossproduct-structure-of-kappa-poincare-group-and-non-1buvbvbwmt.pdf

Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry

The $\kappa$-deformation of the D-dimensional Poincar\'e algebra $(D\geq 2)$ with any signature is given. Further the quadratic Poisson brackets, determined by the classical $r$-matrix are calculated, and the quantum Poincar\'e group "with noncommuting parameters" is obtained.

/pdf/quantum-kappa-poincare-in-any-dimensions-4ytozs9v22.pdf

Quantum $\kappa$-Poincare in Any Dimensions

The ideas underlying the Skyrme model for baryons are introduced. Applications for the properties of single baryons (B=1) in the case of two and three flavours are based on Skyrme's hedgehog ansatz. The interaction between two baryons is discussed within the product ansatz for the B=2 system. The pion-baryon S-matrix is derived in the adiabatic approximation. The possibility to include quark degrees of freedom is shown in terms of the hybrid model. Finally the origin and implications of the Wess Zumino-Witten action are presented.

https://iopscience.iop.org/article/10.1088/0034-4885/49/8/001/pdf

Baryons in the Skyrme Model

Following the construction of the $\kappa$-Minkowski space from the bicrossproduct structure of the $\kappa$-Poincare group, we investigate possible differential calculi on this noncommutative space. We discuss then the action of the Lorentz quantum algebra and prove that there are no 4D bicovariant differential calculi, which are Lorentz covariant. We show, however, that there exist a five-dimensional differential calculus, which satisfies both requirements. We study also a toy example of 2D $\kappa$-Minkowski space and and we briefly discuss the main properties of its differential calculi.

Noncommutative Differential Calculus on the Kappa-Minkowski Space

The Dirac-Coulomb problem for the κ-Poincaré quantum group

Consequences of the Pauli principle applied to a quark model analysis of light hypernuclei

We investigate the low-lying rotational and vibrational excitations in the Skyrme-Witten model for baryons. The rotational and vibrational motions are found to be strongly coupled, qualitatively changing the decoupled spectrum, so as to produce reasonable agreement with the observed low-lying spectrum.

L. C. Biedenharn

Papers

The Dirac-Coulomb problem for the κ-Poincaré quantum group

Consequences of the Pauli principle applied to a quark model analysis of light hypernuclei

Rotational-vibrational coupling in the Skyrme-soliton model for baryons

Monopolar harmonics in SUsub(f)(3) as eigenstates of the Skyrme-Witten model for baryons

Baryons as Quarks in a Skyrmion Bubble