## On the Coupling Constants, Geometric Probability and Complex Domains

**Authors:** Carlos Castro

By recurring to Geometric Probability methods it is shown that the coupling constants,
α_{EM}, α_{W}, α_{C}, associated with the electromagnetic, weak and strong (color) force
are given by the ratios of measures of the sphere S^{2} and the Shilov boundaries
Q_{3} = S^{2} x RP^{1}, squashed S^{5}, respectively, with respect to the Wyler measure
Ω_{Wyler}[Q_{4}] of the Shilov boundary Q_{4} = S^{3} x RP^{1} of the poly-disc D_{4} (8 real dimensions).
The latter measure Ω_{Wyler}[Q_{4}] is linked to the geometric coupling strength
α_{G} associated to the gravitational force. In the conclusion we discuss briefly other
approaches to the determination of the physical constants, in particular, a program
based on the Mersenne primes p-adic hierarchy. The most important conclusion of
this work is the role played by higher dimensions in the determination of the coupling
constants from pure geometry and topology alone and which does not require to invoke
the anthropic principle.

**Comments:** 9 pages, This article appeared in Progress in Physics vol. 2 April (2006) 46-53

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### Submission history

[v1] 3 Sep 2009

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