Conformal Geometry and Invariants of 3-strand Brownian Braids

Details Conformal Geometry and Invariants of 3-strand Brownian Braids Conformal Geometry and Invariants of 3-strand Brownian Braids

2004-07-02

arxiv.org/abs/hep-th/0407008v1

Nucl.Phys. B714 (2005) 336-356

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 4 figures

Scientific paper

10.1016/j.nuclphysb.2005.02.019

We propose a simple geometrical construction of topological invariants of 3-strand Brownian braids viewed as world lines of 3 particles performing independent Brownian motions in the complex plane z. Our construction is based on the properties of conformal maps of doubly-punctured plane z to the universal covering surface. The special attention is paid to the case of indistinguishable particles. Our method of conformal maps allows us to investigate the statistical properties of the topological complexity of a bunch of 3-strand Brownian braids and to compute the expectation value of the irreducible braid length in the non-Abelian case.

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