Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSU(3) density matrix theory
53
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The irreducible representations of the Lie algebra ${frak su}$(3) describe rotational bands in the context of the nuclear shell and interacting boson models. The density matrices associated with ${frak su}$(3) provide an alternative theoretical framework for obtaining these bands. The ${frak su}$(3) density matrix formulation is mathematically simpler than representation theory, yet it yields similar results. Bands are solutions to a system of polynomial equations defined by the quadratic and cubic ${frak su}$(3) Casimirs. Analytic solutions are found in many physically important cases including rotation about principal axes and spheroids. Numerical solutions are reported in other cases including tilted rotors. The physics of rotational bands is more transparent in the presented formalism. In representation theory bands terminate because the space is finite-dimensional. In ${frak su}$(3) density matrix theory bands terminate when faster rotation produces a spheroid rotating around its symmetry axis.
rate research
Read More
Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the $19$ low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-to-leading order~cite{Ren:2014vea} is supported by comparing the effective parameters (the combinations of the $19$ couplings) with the corresponding low-energy constants in the SU(2) sector~cite{Alvarez-Ruso:2013fza}. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref.~cite{Alvarez-Ruso:2013fza}.
For a $Q cdot Q$ interaction the energy weighted sum rule for isovector orbital magnetic dipole transitions is proportional to the difference $sum B(E2, isoscalar) - sum B(E2, isovector)$, not just to $sum B(E2, physical)$. This fact is important in ensuring that one gets the correct limit as one goes to nuclei, some of which are far from stability, for which one shell (neutron or proton) is closed. In $0p$ shell calculations for the even-even Be isotopes it is shown that the Fermion SU(3) model and Boson SU(3) model give different results for the energy weighted scissors mode strengths.
A group of fuzzy spacetime with SU(3) isometry is studied at the two loop level in IIB matrix model. It consists of spacetime from 4 to 6 dimensions, namely from CP2 to SU(3)/U(1)x U(1). The effective action scales in a universal manner in the large N limit as N and N^{4/3} on 4 and 6 dimensional manifolds respectively. The 4 dimensional spacetime CP2 possesses the smallest effective action in this class.
We investigate the quantum entanglement entropy for the four-dimensional Euclidean SU(3) gauge theory. We present the first non-perturbative calculation of the entropic $c$-function ($C(l)$) of SU(3) gauge theory in lattice Monte Carlo simulation using the replica method. For $0 leqslant l leqslant 0.7$~fm, where $l$ is the length of the subspace, the entropic $c$-function is almost constant, indicating conformally invariant dynamics. The value of the constant agrees with that perturbatively obtained from free gluons, with 20 % discrepancy. When $l$ is close to the Hadronic scale, the entropic $c$-function decreases smoothly, and it is consistent with zero within error bars at $l gtrsim 0.9$ fm.
We study baryon-baryon scattering by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. We derive the corresponding diagrammatic rules paying special attention to complications caused by momentum-dependent interactions and propagators of particles with non-zero spin. We define the effective potential as a sum of two-baryon irreducible contributions of time-ordered diagrams and derive a system of integral equations for the scattering amplitude, which provides a coupled-channel generalization of the Kadyshevsky equation. The obtained leading-order baryon-baryon potentials are perturbatively renormalizable, and the corresponding integral equations have unique solutions in all partial waves. We discuss the issue of additional finite subtractions required to improve the ultraviolet convergence of (finite) loop integrals on the example of nucleon-nucleon scattering in the $^3P_0$ partial wave. Assuming that corrections beyond leading order can be treated perturbatively, we obtain a fully renormalizable formalism which can be employed to study baryon-baryon scattering.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
