Gauge-Invariant Brout--Englert--Higgs Mechanism without Spontaneous Breaking of Local Gauge Symmetry: A Quantum-Reference-Frame Formulation
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)em Gauss law: W± 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.
Related
- Spontaneous symmetry breaking as a mechanism for the Gribov scale in a BRST-invariant formulation
- Spontaneous particle-hole symmetry breaking in a disordered two-site quantum breakdown model
- Persistent Spontaneous Time-Reversal Breaking
- Spontaneous persistent currents and time-reversal symmetry breaking in thick-walled Weyl semimetal cylinders
- Can Spontaneous Time-Translation Symmetry Breaking Be Quantized Without Explicit Branches?
BibTeX
@misc{kondo2026gaugeinvariant,
title = {{Gauge-Invariant Brout--Englert--Higgs Mechanism without Spontaneous Breaking of Local Gauge Symmetry: A Quantum-Reference-Frame Formulation}},
author = {Kei-Ichi Kondo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17264},
eprint = {2610.17264},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17264},
}
RIS
TY - UNPB
TI - Gauge-Invariant Brout--Englert--Higgs Mechanism without Spontaneous Breaking of Local Gauge Symmetry: A Quantum-Reference-Frame Formulation
AU - Kei-Ichi Kondo
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17264
UR - https://arxiv.org/abs/2610.17264
AB - 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)_em Gauss law: W^± 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.
ER -