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p-adic string compactified on a torus. (English) Zbl 0703.22010
This is one of many recent papers devoted to study the non-archimedean string theory. The $$[U(1)]^ D$$ model with the Villain form of action on a g-loop generalization of the Bruhat-Tits tree for the p-adic linear group $$GL(2,{\mathbb{Q}}_ p)$$ is considered. The statistical sum and all correlation functions are calculated. The amplitude for the emission of N particles from the boundary of the Bruhat-Tits generalized tree is presented. The method of calculating consists in considering first the finite connected subgraph, determining the statistical sum and correlators for this graph and taking the limit.
Reviewer: P.Maślanka

##### MSC:
 22E35 Analysis on $$p$$-adic Lie groups 83E30 String and superstring theories in gravitational theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81S20 Stochastic quantization
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