2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201501Based on the decomposition of U(1) gauge potential theory and the $ϕ$-mapping topological current theory, the three-dimensional knot invariant and a four-dimensional new topological invariant are discussed in the U(1) gauge field.10 pages, 0 figures accepted by MPLAHigh Energy Physics - Theorytext