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

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 (D...

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Bibliographic Details
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
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Summary: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.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-020-00955-9