The symplictic vacuum, exotic quasi particles and gravitational instanton

Abstract

Abstract Various experimental studies conducted in the eighties indicated the existence of certain anomalous positron production which could not be accounted for within the generally accepted framework of the standard model. Subsequently several theories were advanced by different investigators notably in Darmstadt, Frankfurt and Cairo to explain the new phenomenon and a neutral meson with a mass equal to 1.8 MeV was predicted by a German group around Greiner and his associates. Concurrently to this development, and seemingly independent of it, some fundamental work by `t Hooft in Utrecht and subsequent studies by Peccei and Quinn in Stanford led Weinberg in Austin to postulate the existence of a new particle which was christened by Wilczek and him the axion. We note that the connection between the Darmstadt–Frankfurt–Cairo–Bristol neutral boson and the axion was not immediately recognized although even a fleeting glance would have revealed the similarity, particularly because the neutral boson was estimated to have a mass of about m =1.8 MeV while the mass of the axion was also conjectured to be m a =1.8 MeV. The present work draws attention to the possibility of relating the said anomalous positron production to certain types of topological defects in the so-called symplictic vacuum of E Infinity theory. These defects, which could be interpreted physically as exotic quasi particles or mini black holes pair production, are created via the instanton mechanism rather than the usual classical gravitational collapse. In turn these “mini” black holes and or exotic particles are perceived experimentally, as an increased rate in the positron production which is not entirely surprising when we note that electrons may be modelled using some forms of mini black hole. The same processes may be seen in a different way as a continuous symmetry breaking of the symmetry on average of the ramified hyperbolic “tiling” geometry of the VAK of the E Infinity vacuum. That means the vacuum fluctuation is the “mechanism” of the symmetry breaking of the VAK. Since symmetry breaking is always accompanied physically by the appearance of a new particle, this VAK fluctuation produces a large family of such symmetry breaking particles of which the axion of the P–Q symmetry breaking is but one of many others. In this manner, the excess production in positrons may be attributed to the disintegration of particles such as the axion which in turn are a consequence of the continuous disintegration and reformation of the symplictic E Infinity VAK via the continuous symmetry breaking vacuum fluctuation. Of course, it is a well-known fact that in the classical limit the rate of production of the aforementioned black holes equals that of ordinary quantum field theory in the sense of Schwinger. However, from a number theoretical view point, E Infinity theory is effectively an extension of quantum field theory into the irrational domain and prior to such limit there is the possibility of a considerably large black hole pair production which could be observed and may be interpreted as anomalous positron production in an experiment using a stack of nuclear emulsions exposed for instance to a beam of 12 C or 22 Ne ions as done by El-Nadi et al. at Cairo University rather than using modern electronic detectors joined to a huge heavy ion accelerator. The paper concludes with observing that the complex symplictic modular group could be used to unify quantum mechanics and general relativity.