Classical charged particle models derived from complex shift methods

Extended charged objects embedded in complex space-time are proposed using the double-copy or complex shift method. Most of the objects studied are 3D bosonic strings in different shapes. The most detailed case studied is a static charged open bosonic string. It is found that this can be interpreted purely electromagnetically. It exhibits the same relation between charge, mass, angular momentum, and magnetic moment as the Dirac equation and the Kerr-Newman metric. The spin of the particle is purely electromagnetic, as is the mass. A gyromagnetic ratio of 2 is obtained. The fields in this case are multi-valued, and the singular part of the fields can be arranged to be on an unphysical Riemann sheet with judicious selection of Riemann cut surfaces. The calculations of mass and angular momentum are done numerically using multi-precision algorithms. The mass calculation agrees with the measured electron mass to an accuracy of about 3 electron volts.

Particles for knotted or linked strings in 3 space dimensions are also proposed, and these inherit the topological invariants of the knot or link they are based on. A liquid drop model with complex shift is also discussed.

The multi-valued behavior of the solutions, related to that of the Kerr-Newman metric, can be thought of as the origin of the Einstein-Rosen bridge, and the conjectures that this is the origin of quantum entanglement, ER=EPR, is therefore supported in this theory. So we have here a classical theory which has some properties of quantum mechanics. Hopefully it can offer a new phenomenological application of string theory as a semiclassical model for elementary particles, nuclei, and solitons in condensed matter, fluids, and gases.