Charge Before U(1) Symmetry: Noether Correspondence in a Pre-Spacetime Scalar-Field Theory

This paper is archived as a speculative research work. Electric charge is conventionally represented in continuum field theory by a matter-field U(1) weight whose global symmetry yields a conserved Noether current. This paper develops the correspondence in the opposite explanatory direction. Within the declared handedness-readable bounded-support domain of the Scalar-Field framework, a completed rank-3 support possesses one of two opposite handedness classes, H_B=±1 . From the phase-completed handedness report we obtain a signed bounded-support charge class, Q_b(B)=H_B, before introducing any continuum gauge symmetry, spinor field, or Noether current. On the declared fixed closed transition domain, persistent support histories preserve this class and certified conjugate formation and removal events contribute zero net charge, yielding finite SF charge conservation, Δ Q_ SF( )=0. A selected finite electrodynamics representation then carries the same class as the normalized relative- U(1) weight, q_B=Q_b(B)=H_B. The corresponding fixed-weight Maxwell–Dirac sector has the standard global U(1) symmetry and canonical Noether current j_B^ = Q_b(B) _B ^ _B, _ j_B^ =0 on shell. Under the explicit one-support continuum normalization ∈t_ _B ^ _B\,d _ = 1, the integrated continuum charge reproduces the originating SF charge class, and finite inventories satisfy Q_U(1)( )=Q_ SF( ). The resulting Charge–Noether correspondence therefore establishes a derivationally prior SF charge antecedent, its finite conservation, its recognition as a relative- U(1) matter weight, and its recovery as normalized integrated Noether charge. We interpret the conserved histories of handed bounded supports as the SF-native physical antecedent represented by the continuum charge-current description; this interpretation does not assert a pointwise map from those histories to the Dirac current. The construction preserves a strict distinction between SF-native physical structure and continuum interface representation and does not claim a primitive SF U(1) , a pointwise SF–Dirac current identity, a derivation of the electromagnetic coupling e , or a complete derivation of electrodynamics.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-04
DOI
https://doi.org/10.5281/zenodo.22314124
Primary Topic
Quantum and Classical Electrodynamics
Type
preprint
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preprint

Charge Before U(1) Symmetry: Noether Correspondence in a Pre-Spacetime Scalar-Field Theory

Michael E. Labhard
Zenodo (CERN European Organization for Nuclear Research)
Quantum and Classical Electrodynamics
preprint

Charge Before U(1) Symmetry: Noether Correspondence in a Pre-Spacetime Scalar-Field Theory

Michael E. Labhard
preprint en

Abstract

This paper is archived as a speculative research work. Electric charge is conventionally represented in continuum field theory by a matter-field U(1) weight whose global symmetry yields a conserved Noether current. This paper develops the correspondence in the opposite explanatory direction. Within the declared handedness-readable bounded-support domain of the Scalar-Field framework, a completed rank-3 support possesses one of two opposite handedness classes, H_B=±1 . From the phase-completed handedness report we obtain a signed bounded-support charge class, Q_b(B)=H_B, before introducing any continuum gauge symmetry, spinor field, or Noether current. On the declared fixed closed transition domain, persistent support histories preserve this class and certified conjugate formation and removal events contribute zero net charge, yielding finite SF charge conservation, Δ Q_ SF( )=0. A selected finite electrodynamics representation then carries the same class as the normalized relative- U(1) weight, q_B=Q_b(B)=H_B. The corresponding fixed-weight Maxwell–Dirac sector has the standard global U(1) symmetry and canonical Noether current j_B^ = Q_b(B) _B ^ _B, _ j_B^ =0 on shell. Under the explicit one-support continuum normalization ∈t_ _B ^ _B\,d _ = 1, the integrated continuum charge reproduces the originating SF charge class, and finite inventories satisfy Q_U(1)( )=Q_ SF( ). The resulting Charge–Noether correspondence therefore establishes a derivationally prior SF charge antecedent, its finite conservation, its recognition as a relative- U(1) matter weight, and its recovery as normalized integrated Noether charge. We interpret the conserved histories of handed bounded supports as the SF-native physical antecedent represented by the continuum charge-current description; this interpretation does not assert a pointwise map from those histories to the Dirac current. The construction preserves a strict distinction between SF-native physical structure and continuum interface representation and does not claim a primitive SF U(1) , a pointwise SF–Dirac current identity, a derivation of the electromagnetic coupling e , or a complete derivation of electrodynamics.

Zenodo (CERN European Organization for Nuclear Research)
Life in Land
Quantum and Classical Electrodynamics
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