A stochastic derivation of the geodesic rule

Details A stochastic derivation of the geodesic rule A stochastic derivation of the geodesic rule

2006-02-09

arxiv.org/abs/hep-th/0602085v1

Int.J.Mod.Phys.A21:1493-1502,2006

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, No figures. To be published in Int. Jour. Mod. Phys. A

Scientific paper

10.1142/S0217751X06031740

We argue that the geodesic rule, for global defects, is a consequence of the randomness of the values of the Goldstone field $\phi$ in each causally connected volume. As these volumes collide and coalescence, $\phi$ evolves by performing a random walk on the vacuum manifold $\mathcal{M}$. We derive a Fokker-Planck equation that describes the continuum limit of this process. Its fundamental solution is the heat kernel on $\mathcal{M}$, whose leading asymptotic behavior establishes the geodesic rule.

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