Quantum SU(3) Skyrme model with noncanonical embedded SO(3) soliton

The new ansatz which is the SO(3) group soliton was defined for the SU(3) Skyrme model. The model is considered in noncanonical bases $SU(3)\supset SO(3)$ for the state vectors. A complete canonical quantization of the model have been investigated in the collective coordinate formalism for the fundamental SU(3) representation of the unitary field. The independent quantum variables manifold cover all the eight dimensions SU(3) group manifold due to the new ansatz. The explicit expressions of the Lagrangian and Hamiltonian densities are derived for this modified quantum skyrmion.Comment: 8 RevTex4 pages, no figure

Noncanonicaly Embedded Rational Map Soliton in Quantum SU(3) Skyrme Model

The quantum Skyrme model is considered in non canonical bases SU(3) > SO(3) for the state vectors. A rational map ansatz is used to describe the soliton with the topological number bigger than one. The canonical quantization of the Lagrangian generates in Hamiltonian five different "moments of inertia" and negative quantum mass corrections, which can stabilize the quantum soliton solution. Explicit expressions of the quantum Lagrangian and the Hamiltonian are derived for this model soliton.Comment: 11 RevTex4 pages, no figure

Nucleon form factors in the canonically quantized Skyrme model

The explicit expressions for the electric, magnetic, axial and induced pseudoscalar form factors of the nucleons are derived in the {\it ab initio} quantized Skyrme model. The canonical quantization procedure ensures the existence of stable soliton solutions with good quantum numbers. The form factors are derived for representations of arbitrary dimension of the SU(2) group. After fixing the two parameters of the model, $f_\pi$ and $e$, by the empirical mass and electric mean square radius of the proton, the calculated electric and magnetic form factors are fairly close to the empirical ones, whereas the the axial and induced pseudoscalar form factors fall off too slowly with momentum transfer.Comment: 14pp including figure

Coupling coefficients of SO(n) and integrals over triplets of Jacobi and Gegenbauer polynomials

The expressions of the coupling coefficients (3j-symbols) for the most degenerate (symmetric) representations of the orthogonal groups SO(n) in a canonical basis (with SO(n) restricted to SO(n-1)) and different semicanonical or tree bases [with SO(n) restricted to SO(n'})\times SO(n''), n'+n''=n] are considered, respectively, in context of the integrals involving triplets of the Gegenbauer and the Jacobi polynomials. Since the directly derived triple-hypergeometric series do not reveal the apparent triangle conditions of the 3j-symbols, they are rearranged, using their relation with the semistretched isofactors of the second kind for the complementary chain Sp(4)\supset SU(2)\times SU(2) and analogy with the stretched 9j coefficients of SU(2), into formulae with more rich limits for summation intervals and obvious triangle conditions. The isofactors of class-one representations of the orthogonal groups or class-two representations of the unitary groups (and, of course, the related integrals involving triplets of the Gegenbauer and the Jacobi polynomials) turn into the double sums in the cases of the canonical SO(n)\supset SO(n-1) or U(n)\supset U(n-1) and semicanonical SO(n)\supset SO(n-2)\times SO(2) chains, as well as into the_4F_3(1) series under more specific conditions. Some ambiguities of the phase choice of the complementary group approach are adjusted, as well as the problems with alternating sign parameter of SO(2) representations in the SO(3)\supset SO(2) and SO(n)\supset SO(n-2)\times SO(2) chains.Comment: 26 pages, corrections of (3.6c) and (3.12); elementary proof of (3.2e) is adde

The induced representations of Brauer algebra and the Clebsch-Gordan coefficients of SO(n)

Induced representations of Brauer algebra $D_{f}(n)$ from $S_{f_{1}}\times S_{f_{2}}$ with $f_{1}+f_{2}=f$ are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients (ORCs) of $S_{f_{1}}\times S_{f_{2}}\uparrow D_{f}(n)$ with $f\leq 4$ up to a normalization factor are derived by using the linear equation method. Weyl tableaus for the corresponding Gel'fand basis of SO(n) are defined. The assimilation method for obtaining CG coefficients of SO(n) in the Gel'fand basis for no modification rule involved couplings from IDCs of Brauer algebra are proposed. Some isoscalar factors of $SO(n)\supset SO(n-1)$ for the resulting irrep $[\lambda_{1},~\lambda_{2},~ \lambda_{3},~\lambda_{4},\dot{0}]$ with $\sum\limits_{i=1}^{4}\lambda_{i}\leq .Comment: 48 pages latex, submitted to Journal of Phys.

Host-Microbe Co-metabolism Dictates Cancer Drug Efficacy in C. elegans

Fluoropyrimidines are the first-line treatment for colorectal cancer, but their efficacy is highly variable between patients. We queried whether gut microbes, a known source of inter-individual variability, impacted drug efficacy. Combining two tractable genetic models, the bacterium E. coli and the nematode C. elegans, we performed three-way high-throughput screens that unraveled the complexity underlying host-microbe-drug interactions. We report that microbes can bolster or suppress the effects of fluoropyrimidines through metabolic drug interconversion involving bacterial vitamin B-6, B-9, and ribonucleotide metabolism. Also, disturbances in bacterial deoxynucleotide pools amplify 5-FU-induced autophagy and cell death in host cells, an effect regulated by the nucleoside diphosphate kinase ndk-1. Our data suggest a two-way bacterial mediation of fluoropyrimidine effects on host metabolism, which contributes to drug efficacy. These findings highlight the potential therapeutic power of manipulating intestinal microbiota to ensure host metabolic health and treat disease.Peer reviewe