Quantized space-time and consequences

Abstract

We present a concrete quantized space-time at small distances. After transition to the large scale of nonquantized space-time, this method gives rise to a changed momentum operator which in turn leads to new infinite order differential equations describing extended (nonlocal) fields. The Green's functions of these equations are finite in the Euclidean momentum space, which provides for the construction of the theory of interacting fields free from ultraviolet divergences. In our scheme, interaction laws (e.g., the Coulomb, Yukawa potentials) between two particles are changed and have an attractive nature at small distances. As an example of this, finite quantum electrodynamics is constructed within the framework of quantized space-time. Restrictions on the parameterl of the theory are obtained:l < 10−16 cm. Our scheme contains some interesting possibilities: description of quarks, gluons and tachyon-type objects, and indication of a way to a solution of the problem of quantization of particle mass and of quark confinement. Moreover, within the model one can obtain the scalesEEW∼ 118.1 GeV andEEW∼5353 GeV of the unification of electromagnetic and weak, and weak and nuclear processes, respectively. The last possibility is very interesting for the experimental verification of the theory.