March 2025 - Electromagnetic Fine-Structure Constant
The simplified case, in which the physics is governed by a single gauge theory SU(2) derives from the dual charge of the system. A (anti)monopole is immersed into the blob at deconfining phase at 1.32 * critical temperature. All charges considered, considering only a trapped monopole suffices. At this temperature, the pressure vanishes, and the shell experiences high conductance, which can be used to approximate the blob charge for probes of long wavelengths. A mirror charge construction for boundary conditions on a spherical surface is generated with the classical Coulomb potentials, carrying a Yukawa factor for the association with the monopole's charge, so that it can be treated as unity. This includes the screening length in the exponential, which arises from other screened and stable dipoles in the infinite-volume plasma. If it's much larger than the Bohr radius, the blob radius in pure SU(2) is
The effective charge of the blob at bulk critical temperature is subject to screening, and superconductivity of the boundary shell. Outside of the blob, it applies an electrical potential
Which itself can be developed into forms explicitly dependent on the coordinates. A blob with a trapped monopole, is not thermalized when it forms, and the monopole's location is equally likely within the blob apart from a thin boundary shell, in which the Hagedorn transition takes place. A blob in itself contains all three phases. The boundary shell is characterized by decoupled dual Abelian gauge modes, and can't be redistributed into the interior of the blob. After bulk thermalization, a thick boundary shell with a temperature gradient and phase mixing forms instead. Trapped monopoles entering it will rapidly change.
After bulk thermalization, the monopole is kicked toward the thick boundary shell, where its mass and charge are reduced, until it becomes part of the condensate contributing to the phase mixture. To conserve charge and blob mass, another monopole in the condensate acts in place of the original monopole in the deconfining bulk of the blob. Physically, it's subject to mixing of two thermal SU(2) gauge theories, one for electrons, and one for the CMB. The nonthermal probe field always resides in the electron field, and is only sensitive to the physics of SU(2)e fields in the blob.
The blob's effective charge is represented as an angular and radial average wrt. the probability density prior to thermalization. The angular average of the potential yields that there is no dipole/quadrupole contribution to the electric charge distribution. This in turn establishes the mean radial position and charge averaged over a full probe oscillation. With these, the finestructure constant can be defined.
This finestructure constant is too low (expect 137), so the thick boundary shell is expected to have significant effects on these quantities. Since isolated monopoles can't exist in the thick boundary shell, introduce a correction to the thin-shell approximation of the blob charge
Which is still too low. This is an indicator that the mixing effects might also contribute significantly.