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arXiv · 2610.17264

Gauge-Invariant Brout--Englert--Higgs Mechanism without Spontaneous Breaking of Local Gauge Symmetry: A Quantum-Reference-Frame Formulation

Kei-Ichi Kondo
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Abstract

The Brout--Englert--Higgs (BEH) mechanism can be formulated in gauge-invariant relational terms without assigning physical spontaneous breaking to a local gauge redundancy. We treat the gauge orientation of the Higgs field as dynamical internal reference data and describe the gauge connection relative to this Higgs frame. On a regular patch where the frame exists, the Higgs kinetic term induces a positive-semidefinite mass-squared quadratic form on the gauge-orbit directions and reproduces the standard tree-level vector masses. A complete Higgs frame yields a gauge-invariant relational connection, whereas a partial frame is defined only up to a stabilizer group $H$ and produces Higgs stiffness only along the coset directions $G/H$. In quantum field theory the normalized frame and relational connection are nonpolynomial composite variables; physical masses are therefore characterized through suitably renormalized gauge-invariant composite correlators, or through fully dressed operators in residual-charged sectors. Applying this construction to the electroweak theory, we show that the Higgs frame relationalizes the $SU(2)_L$ redundancy while leaving a residual electromagnetic $U(1)_{\rm em}$ Gauss law: $W^\pm$ and charged fermionic modes require electromagnetic dressing, whereas neutral channels admit local gauge-invariant interpolators. This formulation connects Higgs dressings, FMS composites, and internal quantum-reference-frame language while keeping local mass generation distinct from global symmetry realization and topological obstructions.

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Kei-Ichi Kondo. 2026-10-12. Gauge-Invariant Brout--Englert--Higgs Mechanism without Spontaneous Breaking of Local Gauge Symmetry: A Quantum-Reference-Frame Formulation. https://arxiv.org/abs/2610.17264

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