Global Evolution of the U(1) Higgs Boson: Nonlinear Stability and Uniform Energy Bounds

• Published in: Annales Henri Poincaré 2021-03, Vol.22 (3), p.677-713
• Main Authors: Dong, Shijie, LeFloch, Philippe G., Wyatt, Zoe
• Format: Article
• Language: English
• Subjects: Bosons; Boundary value problems; Classical and Quantum Gravitation; Dirac equation; Dynamical Systems and Ergodic Theory; Electroweak interactions (field theory); Electroweak model; Elementary Particles; Higgs bosons; Mathematical and Computational Physics; Mathematical Methods in Physics; Minkowski space; Original Paper; Physics; Physics and Astronomy; Quantum Field Theory; Quantum Physics; Relativity Theory; Stability; Theoretical
• ISSN: 1424-0637; 1424-0661
• DOI: 10.1007/s00023-020-00955-9

Relying on the hyperboloidal foliation method, we establish the nonlinear stability of the ground state of the U (1) standard model of electroweak interactions. This amounts to establishing a global-in-time theory for the initial value problem for a nonlinear wave–Klein–Gordon system that couples (Dirac, scalar, gauge) massive equations together. In particular, we investigate here the Dirac equation and study a new energy functional defined with respect to the hyperboloidal foliation of Minkowski spacetime. We provide a decay result for the Dirac equation which is uniform in the mass coefficient and thus allows for the Dirac mass coefficient to be arbitrarily small. Furthermore, we establish energy bounds for the Higgs fields and gauge bosons that are uniform with respect to the hyperboloidal time variable.