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A stochastic derivation of the geodesic rule

Nikos Kalogeropoulos
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Abstract

We argue that the geodesic rule, for global defects, is a consequence of the randomness of the values of the Goldstone field $ϕ$ in each causally connected volume. As these volumes collide and coalescence, $ϕ$ 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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Nikos Kalogeropoulos. 2006-02-09. A stochastic derivation of the geodesic rule. https://doi.org/10.1142/s0217751x06031740

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