Gauge Abelian Models for Symetry Objects

Abstract

This work explores gauge symmetry for the so-called symmetry object. The investigation associates gauge symmetry to a collection of fields. Different fields are boxed inside of a symmetry object as a matrix. A systemic gauge symmetry is proposed. It introduces a new procedure where gauge symmetry should not be restricted to Yang-Mills procedure. Two fields arrangements are taken. The N-matter fields and M- mediators fields. These two symmetry objects are connected through an abelian gauge symmetry. The corresponding generator becomes a matricial charge Q rotating as U = eiQα  where α means the abelian gauge parameter. It yields a collective gauge transformation. Thus, instead of considering the Yang-Mills canonical procedure where the number of gauge fields is equal to the number of gauge generators, this work develops an abelian gauge theory for symmetry objects. The cases where Q is 2x2 and 3x3 matrices are studied. By consequence, instead of developing gauge models where three and eight mediators should be associated to SU(2) and SU(3) groups, are develops their behaviors in terms M an abelian group.