Renormalization group treatment of polymer excluded volume by t’Hooft–Veltman-type dimensional regularization

The chain conformation space renormalization group method is transformed into a representation where the t’Hooft–Veltman method of dimensional regularization can directly be applied to problems involving polymer excluded volume. This t’Hooft–Veltman-type representation enables a comparison to be made with other direct renormalization methods for polymer excluded volume. In contrast to the latter, the current method and the chain conformation one from which it is derived are not restricted to the asymptotic limit of very long chains and do not require the cumbersome use of insertions to calculate the relevant exponents. Furthermore, the theory emerges directly in polymer language from the traditional excluded volume perturbation expansion which provides the correct weight factors for the diagrams. Special attention is paid to the general diagrammatic structure of the theory and to the renormalization prescription in order that this prescription follows from considerations on measurable quantities. The theory is illustrated by calculation of the mean square end-to-end distance and second virial coefficient to second order including the full crossover dependence on the renormalized strength of the excluded volume interaction and on the chain length. A subsequent paper provides the generalization of the theory to the treatment of excluded volume effects in polyelectrolytes.