On several parameter renormalization group equations and renormalization scheme specifications

An example of the explicit realization of the full renormalization group for physical quantities is investigated. It introduces two-index beta functions beta /sub ij/(g/sub j/): (i) the first index specifying the renormalization scheme chosen (including the scale mu ); (ii) the second index specifying the coupling of which the appropriate beta function is the differential transformation. The treated example is presented in a 4- epsilon dimensional O(n) massless ( phi * phi )/sup 2/ theory with emphasis on the calculation of the fixed point.