The number of the hyperbranched polymers in the system is investigated for the polymerization process to give the asymptotic form of the concentration of the n-mer. The polydispersity exponent is calculated, which coi...The number of the hyperbranched polymers in the system is investigated for the polymerization process to give the asymptotic form of the concentration of the n-mer. The polydispersity exponent is calculated, which coincides with that of the classical result. Finally, the asymptotic forms of the number, the weight and the z-average degrees of the polymerization were evaluated analytically to obtain polydispersity index, which is close to 1 as the reaction is quantitatively completed.展开更多
We revisit quantum gravitational contributions to quantum gauge field theories in the gauge condition independent Vilkovisky-DeWitt formalism based on the background field method.With the advantage of Landau-DeWitt ga...We revisit quantum gravitational contributions to quantum gauge field theories in the gauge condition independent Vilkovisky-DeWitt formalism based on the background field method.With the advantage of Landau-DeWitt gauge,we explicitly obtain the gauge condition independent result for the quadratically divergent gravitational corrections to gauge couplings.By employing,in a general way,a scheme-independent regularization method that can preserve both gauge invariance and original divergent behavior of integrals,we show that the resulting gauge coupling is power-law running and asymptotically free.The regularization scheme dependence is clarified by comparing with results obtained by other methods.The loop regularization scheme is found to be applicable for a consistent calculation.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.20574016 and 20303006)the Natural Science Foundation of Hebei Province(Grant Nos.201072 and B2004000093).
文摘The number of the hyperbranched polymers in the system is investigated for the polymerization process to give the asymptotic form of the concentration of the n-mer. The polydispersity exponent is calculated, which coincides with that of the classical result. Finally, the asymptotic forms of the number, the weight and the z-average degrees of the polymerization were evaluated analytically to obtain polydispersity index, which is close to 1 as the reaction is quantitatively completed.
基金Supported in part by the National Science Foundation of China under Grant Nos. 10821504,10975170the Key Project of Knowledge Innovation Program of Chinese Academy of Science
文摘We revisit quantum gravitational contributions to quantum gauge field theories in the gauge condition independent Vilkovisky-DeWitt formalism based on the background field method.With the advantage of Landau-DeWitt gauge,we explicitly obtain the gauge condition independent result for the quadratically divergent gravitational corrections to gauge couplings.By employing,in a general way,a scheme-independent regularization method that can preserve both gauge invariance and original divergent behavior of integrals,we show that the resulting gauge coupling is power-law running and asymptotically free.The regularization scheme dependence is clarified by comparing with results obtained by other methods.The loop regularization scheme is found to be applicable for a consistent calculation.
