01 / Gauge
The correction must be built from gauge-invariant fields or controlled symmetry-breaking terms.
Working paper / June 6, 2026
Gauge-Consistent Effective Currents in Five-Dimensional Projection Electromagnetism
A referee-facing effective-current framework for deciding which projected currents are admissible, degenerate, or experimentally separable.
01 / Abstract
Abstract
Five-dimensional projection models of electromagnetism often produce a four-dimensional Maxwell equation with an additional effective current. The difficulty is not writing such a current; the difficulty is writing one that is compatible with four-dimensional gauge invariance, charge conservation, and exact recovery of ordinary Maxwell theory.
Starting from a five-dimensional Maxwell-like system on coordinates \(X^A=(x^\mu,\chi)\), the paper derives a projected equation with a new current \(J^\nu_{\mathrm{new}}\), then imposes local admissibility conditions on that current.
On a contractible four-dimensional patch, every smooth identically conserved correction can be written as the divergence of an antisymmetric polarization tensor, up to singular or boundary-supported terms.
02 / Criteria
Admissible Currents
The paper forces speculative projection currents through ordinary field-theory constraints before treating them as candidate physics.
\[
\nabla_\mu F^{\mu\nu}
= \mu_0\left(J^\nu
+ J^\nu_{\mathrm{new}}\right)
\]
02 / Conservation
It must satisfy charge conservation, or explicitly identify exchange with a bulk or boundary current.
03 / Recovery
It must vanish in the Maxwell recovery limit so ordinary electrodynamics is exact when the fifth sector decouples.
04 / Separability
It should predict parity or scaling diagnostics that separate it from conventional artifacts.
03 / Dictionary
Operator Families
The framework compresses many speculative branches into a smaller set of observational families.
- Scalar Constitutive weighting through fields such as \(Z(s)F^{\mu\nu}\).
- Fifth flow Corrections from fifth gradients or mixed-normal components.
- Curvature Projection-curvature mixing terms tied to embedding geometry.
- Boundary Singular, edge, or boundary-supported corrections that require special tests.
- Higher gradient Short-range or edge-enhanced operators that can mimic material response.
04 / Files
Paper Files
The PDF is generated from the LaTeX source. Both are published for auditability and future revision.