Yang-Mills solutions on Minkowski space via non-compact coset spaces

We find a two-parameter family of solutions of the Yang-Mills equations for gauge group SO(1,3) on Minkowski space by foliating different parts of it with non-compact coset spaces with SO(1,3) isometry. The interior of the lightcone is foliated with hyperbolic space H3 similar to= SO(1, 3)/SO(3), while the exterior of the lightcone employs de Sitter space dS3 similar to= SO(1, 3)/SO(1, 2). The lightcone itself is parametrized by SO(1,3)/ISO(2) in a nilpotent fashion. Equivariant reduction of the SO(1,3) Yang-Mills system on the first two coset spaces yields a mechanical system with inverted double-well potential and the foliation parameter serving as an evolution parameter. Its known analytic solutions are periodic or runaway except for the kink. On the lightcone, only the vacuum solution remains. The constructed Yang-Mills field strength is singular across the lightcone and of infinite action due to the noncompact cosets. Its energy -momentum tensor takes a very simple form, with energy density of opposite signs inside and outside the lightcone.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.