Geometric Necessity of Spontaneous Symmetry Breaking: Three-Stage Derivation of the Higgs Mechanism

Key Points

• This research aims to provide a structural explanation for the Higgs mechanism using geometric concepts.
• Derived three stages of the Higgs mechanism: standing wave vacuum structure, symmetry breaking by scale separation, and mass generation by standing-wave coupling.
• Utilized properties of the hypercube framework to inform the derivation process.
• Established that standing wave vacuum structures lead to symmetry breaking under geometric constraints.
• Demonstrated how mass generation occurs through coupling in a standing wave framework.

Abstract