Calculation of second topological moment of two entangled polymers

Abstract:We set up a field theoretical model based on Abelian Chern-Simons field theories to describe the topological entanglement of two polymers. The topological states of the system are distinguished using the link invariant of Gauss. The second topological moment of the two polymers , where m is the linking number, is exactly computed by field theoretical methods. The result is applied to estimate approximatively the mean square average of the linking number of a polymer P1 in a dilute solution with other polymers.