Quark mixing and exponential form of the Cabibbo-Kobayashi-Maskawa matrix

Various forms of representation of the mixing matrix are discussed. An exponential parametrization e ^ of the Cabibbo-Kobayashi-Maskawa matrix is considered in the context of the unitarity requirement, this parametrization being the most general form of the mixing matrix. An explicit representation for the exponential mixing matrix in terms of the first and second degrees of the matrix  exclusively is obtained. This representation makes it possible to calculate this exponential mixing matrix readily in any order of the expansion in the small parameter λ. The generation of new unitary parametric representations of the mixing matrix with the aid of the exponential matrix is demonstrated.