Quantum geometry of non-archimedean particles and strings

Abstract

An action which is a non-archimedean, ( p-adic) analogue of the worldsheet action of string theory is proposed. Proceeding from this action tree N-point amplitudes are obtained and they are coincident with on-shell tree amplitudes of some non-local scalar field theory. Reality seems to be described by the limit p→1. The above theory becomes local at this limit. There is a metastable state and we find an instanton describing a decay of this state. A p-adic technique is developed.