Polarized Spacetime Foam

TL;DR

This paper models spacetime foam as a dielectric-like medium with quantum handles acting as electric dipoles, leading to finite electric field energy and charge screening effects in spherically symmetric solutions.

Contribution

It introduces a novel approximate model of spacetime foam using scalar and spinor fields, revealing dielectric properties and charge confinement phenomena.

Findings

Electric charge is screened by polarized spacetime foam.

Finite energy of electric fields in the presence of spacetime foam.

Spacetime foam can confine electric fields within a finite region.

Abstract

An approximate model of a spacetime foam is presented. It is supposed that in the spacetime foam each quantum handle is like to an electric dipole and therefore the spacetime foam is similar to a dielectric. If we neglect of linear sizes of the quantum handle then it can be described with an operator containing a Grassman number and either a scalar or a spinor field. For both fields the Lagrangian is presented. For the scalar field it is the dilaton gravity + electrodynamics and the dilaton field is a dielectric permeability. The spherically symmetric solution in this case give us the screening of a bare electric charge surrounded by a polarized spacetime foam and the energy of the electric field becomes finite one. In the case of the spinor field the spherically symmetric solution give us a ball of the polarized spacetime foam filled with the confined electric field. It is shown that the full energy of the electric field in the ball can be very big.