A transformation of the scheme used for regularization and renormalization in a quantum field theory is a map that connects coupling spaces of a theory in different schemes of this type. Especially in quantum chromodynamics, there have been active studies inventing schemes aimed at trying to reduce higher-order corrections in perturbative calculations, which work well for the coupling very close to zero. However, the problem becomes different provided one aims at studying a scheme transformation for values of the coupling away from zero, as is relevant for a vanishing of the beta function away from the origin. It turns out that many existing scheme transformations that work well for the coupling near zero cannot be applied so simply for the coupling away from zero and may cause violation of unitarity and perturbativity in a given theory. Motivated by this, we study the construction of scheme transformations that are applicable in the vicinity of a zero of the beta function away from the origin. We construct and apply scheme transformations at an infrared (IR) zero of the beta function in an vectorial, asymptotically free SU(N) gauge theory with Nf fermions in a representation R to study the scheme dependence of IR-zero. We show that the shift of IR-zero with increasing loop order tends to decrease, providing a quantitative measure of the size of the scheme-dependence in the calculation of IR-zero up to four-loop order at not only small but also moderate coupling away from zero.

As the second part of the thesis work, we study the renormalization-group evolution of a N= 1 supersymmetric SU(N) gauge theory by investigating functions in different schemes [3]. We take two particular schemes and compute Pade approximants to probe the degree of similarity of the respective functions in these schemes.

Finally, we explore the renormalization-group evolution of the Gross-Neveu model with N-component fermions by examining its function up to four-loop order [4]. As part of this study, we apply scheme transformations to this function and also calculate and analyze Pade approximants to the function. From this analysis, we show that there is no evidence for presence of an infrared zero in the nite-N Gross-Neveu model.