1999/06/14 by Franco Ferrari, Ferrari, Franco, I. Lazzizzera +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Topological and Geometric Data Analysis #cond-mat.soft #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.hep-th/9906097
18 pages, latex file + revtex
arxiv created 1999/06/14 · arxiv updated 2009/11/30
In this work we derive certain topological theories of transverse vector fields whose amplitudes reproduce topological invariants involving the interactions among the trajectories of three and four random walks. This result is applied to the construction of a field theoretical model which describes the statistical mechanics of an arbitrary number of topologically linked polymers in the context of the analytical approach of Edwards. With respect to previous attempts, our approach is very general, as it can treat a system involving an arbitrary number of polymers and the topological states are not only specified by the Gauss linking number, but also by higher order topological invariants.