Field Theories of Topological Random Walks

Details Field Theories of Topological Random Walks Field Theories of Topological Random Walks

1999-06-14

arxiv.org/abs/hep-th/9906097v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, latex file + revtex

Scientific paper

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.

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