We impose symmetry principles to elaborate and evaluate the invariance of the Abelian and non-Abelian gauges and evaluate its implications to the laws of physics. The application of the symmetry principle in to the field wich undergoes a rotation in a phase space implies the existence of an Abelian gauge field Meanwhile the application of symmetry principle to the Dirac field as a doublet of SU(2) group implies the existence of a non-Abelian gauge field with structure constant satisfies the Lie group algebra.