Solitonic photons and intermediate vector bosons

Abstract

A four-dimensional topological field theory is introduced which generalises $B\wedge F$ theory to give a Bogomol'nyi structure. A class of non-singular, finite-Action, stable solutions to the variational field equations is identified. The solitonic solutions are analogous to the instanton in Yang-Mills theory. The solutions to the Bogomol'nyi equations in the topologically least complicated $U(1)$ theory have a well-behaved (covariant) phase space of dimension four---the same as that for photons. The dimensional reduction of the four-dimensional Lagrangian is also examined. Bogomol'nyi $U(2)$ solitons resembling the intermediate vector bosons $Z_o$, $W^\pm$ are identified.