Exponents for the excluded volume problem as derived by the dynamic renormalization group method

By regarding the contour length L of a polymer chain as “time”, we derive the mean-square end-to-end distance 〈x²〉 for the polymer chain with excluded volume by means of the dynamic renormalization group. The result to first order in ? = 4 ? d (d is the dimension of the space) is $\text{〈x}{}^2\text{〉 =}\text{const}\text{× L}{}^{\mathrm{<mtext>1+?</mtext><mtext>8</mtext>}}$.