GRADED LIE ALGEBRA AND THE SU(3)_L⊗U(1)_N GAUGE MODEL

Abstract

A classical gauge model based on the Lie group SU (3)L⊗ U (1)N with exotic quarks is reformulated within the formalism of nonassociative geometry associated with an L cycle. The N charges of the fermionic particles and the related parameter constraints are algebraic consequences and are uniquely determined. Moreover, the number of scalar particles is dictated by the nonassociativity of the geometry. As a byproduct of this formalism, the Weinberg angle θw, scalar, charged and neutral gauge boson masses, as well as the mixing angles, are derived. Furthermore, various expressions for the vector and axial couplings of the quarks and leptons with the neutral gauge bosons and lower bounds of the very heavy gauge bosons are obtained.

On the Structure of Graded Lie Triple Systems

“…Since then, many papers describing different physic models by means of graded Lie type structures have appeared, being remarkable the interest on these objects in the last years. For instance, in the case of Lie algebras, we can cite many works related to theory of strings, to color supergravity, to Walsh functions, to electroweak interactions or to gauge models [1,4,9,10,17,18,20,22,25,29,34]. In the case of Lie superalgebras, we can also cite several works modelling continuous suppersymmetry transformations between bosons and fermions or conformal field theory [3,5,19,26,31].…”