Global evolution of the U(1) Higgs boson: nonlinear stability and uniform energy bounds (Q2661999)

The authors study the equations of motion from the Higgs mechanism applied to an abelian \(U(1)\) gauge theory; in particular, a class of nonlinear wave equations which involve the first order Dirac equation coupled to the Klein-Gordon equation is considered. Initial value problems are considered with initial data having small Sobolev norm. The authors establish nonlinear stability of the ground state using a hyperboloidal foliation method. A new decay result is also provided for the Dirac equation; this result is uniform in the mass coefficient. Finally, the authors establish energy bounds for the Higgs fields and gauge bosons.