Gauge-Coupling Normalization Beyond Projector Geometry: Action-Level Typing and Source Factorization

Andrew Morton · Public preprint · Source-normalization criteria

Identifies the source information needed to turn a geometric gauge construction into a physical coupling strength.

Abstract

Gauge fields can emerge from the geometry of a smoothly varying internal subspace, but their coupling strengths are not determined by that geometry alone. Because a spectral projector commutes with its defining operator, that operator has no static light–heavy mixing in its exact spectral decomposition. A nontrivial Schur response must therefore arise from a distinct response operator or from a separately justified non-spectral split. Within the source-induced normalization class considered here, the gauge kinetic coefficient is determined by how the gauge curvature couples to a heavy quadratic response sector. Symmetry constrains the form of this coupling but does not fix its overall magnitude, giving g_H⁻² = λ_H, where λ_H requires independent microscopic source data. The factorized form g_H⁻² = ω_H/τ₀ follows only when an additional relation connects the curvature-source coupling to the projected response of the selected subspace. The analysis therefore distinguishes the geometric origin of gauge fields from the independent dynamical information required to determine their coupling strengths.

Scope

The paper proves why projector geometry alone leaves the coupling magnitude undetermined and states the extra relation required for a shared normalization formula. A physical source and its absolute normalization remain microscopic inputs.

Paper and supporting files

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Gauge-Coupling Normalization Beyond Projector Geometry: Action-Level Typing and Source Factorization

Abstract

Scope

Paper and supporting files

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