We call rectangles Gell-Mann matrices rectangle matrices which make generalization of the expression of a tensor commutation matrix n ⊗ n in terms of tensor products of square Gell-Mann matrices.

There are several reasons to be interested in quantum, nonabelian monopoles. First, if confinement of QCD is a sort of dual superconductor, it is likely to be one of nonabelian variety. Then the effective degrees of freedom involve nonabelian, and not, better understood abelian monopoles. Second, the phenomenon of confinement has to do with fully quantum mechanical, and not semi-classical, beha...

We use the multimonopole moduli space as a tool for studying the properties of BPS monopoles carrying nonabelian magnetic charges. For configurations whose total magnetic charge is purely abelian, the moduli space for nonabelian breaking can be obtained as a smooth limit of that for a purely abelian breaking. As the asymptotic Higgs field is varied toward one of the special values for which the...

The exterior degree d∧(G) of a finite group G has been recently introduced by Rezaei and Niroomand in order to study the probability that two given elements x and y of G commute in the nonabelian exterior square G ∧ G. This notion is related with the probability d(G) that two elements of G commute in the usual sense. Motivated by a paper of Erovenko and Sury of 2008, we compute the exterior deg...

Given a nilpotent Lie algebra L of dimension $$\le 6$$ on an arbitrary field characteristic $$\ne 2$$ , we show direct method to detect whether is capable or not via computations the size its nonabelian exterior square $$L \wedge L$$ . For dimensions higher than 6, result general nature, based evidences low dimensional case, but also large families algebras, namely generalized Heisenberg algebr...

We show that as in abelian gauge fields, nonabelian gauge fields are also trapped on a brane in the Randall-Sundrum model by applying a new mechanism based on topological Higgs mechansim. It is pointed out that although almost massless gauge fields are localized on the brane by the new mechanism, exactly massless gauge fields are not localized. This fact does not yield any problem to abelian ga...