On a connection between the limit set of the Möbius–Klein transformation, periodic continued fractions, El Naschie’s topological theory of high energy particle physics and the possibility of a new axion-like particle

摘要: Abstract In the present work we first give a general representation of derivatives irrational number φ , for instance 1 2 3 etc., as periodic continued fractions. Any can then be expanded in an infinite fraction. The limit set Kleinian transformation acting on E -infinity Cantorian spacetime turned out to this fractions, consequently vacuum is described by set. As discussed El Naschie, every particle interpreted geometrically scaling another. This done using topology hyperbolic space VAK, which nothing but our Here will ratios theoretical masses certain elementary particles that some chosen term . Many these are quite close integer multiples mass particle. Finally discuss possibility new transfinite, axion-like recently Krauss and Naschie [Quintessence, Vintage, London, 1999].