Space-time structure near particles and its influence on particle behavior

Abstract

An interrelation between the properties of the space-time structure near moving particles and their dynamics is discussed. It is suggested that the space-time metric near particles becomes a curved one$\tilde g_{\mu \nu } (x,b_E )$ depending on a random vectorb _E =(b ₄,b) with a distributionw(b ²_E /l ²); the averaged space-time metric$\left\langle {\tilde g_{\mu \nu } (x,b_E )} \right\rangle$ over this distribution gives the general effect on particle behavior. As a result the particle motion in our scheme is described by a nonlinear equation. It turns out that the nonrelativistic limit of this equation gives a simple connection between the space-time structure at small distances and the dynamical behavior of particles. Different types of particle motion (nearly rectilinear, stochastic, and solitonlike) caused by some concrete forms of the averaged conformally flat space-time metric$\left\langle {\tilde g_{\mu \nu } (x,b_E )} \right\rangle$ are considered.