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        "description": "This entry isolates the local phase/potential connection. The original paper's broader electron-mass and gravitational-unification proposals are not certified or adopted wholesale. Maxwell dynamics require the stated action ansatz; local phase freedom alone is not a proof of a unique electromagnetic theory. Later non-Abelian theories remain separate.",
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          "citation": "Hermann Weyl, Elektron und Gravitation I, Zeitschrift für Physik 56 (1929), 330–352; original facsimile in Edition Open Sources",
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      "statement": "# Weyl: local quantum phase and electromagnetic potential\n\nWeyl related position-dependent quantum phase freedom to a compensating electromagnetic potential in covariant differentiation. Simultaneous phase and potential changes preserve the proposed matter action, and the gauge-invariant action is connected with current conservation.\n\nA phase choice that varies from point to point changes how a wave field is differentiated. A corresponding potential change permits a covariant description. Weyl identifies the connection with electromagnetism and relates invariance to conservation within his specified action. This quantum unit-modulus phase construction differs from his earlier real-scale gauge proposal. The April PNAS sketch and the fuller May-received paper belong to one work family.\n\n## Scientific scope\n\nThis entry isolates the local phase/potential connection. The original paper's broader electron-mass and gravitational-unification proposals are not certified or adopted wholesale. Maxwell dynamics require the stated action ansatz; local phase freedom alone is not a proof of a unique electromagnetic theory. Later non-Abelian theories remain separate.\n\n## People and systems\n\nHermann Weyl\n\n\n\n## Original sources\n\n- [Hermann Weyl, Elektron und Gravitation I, Zeitschrift für Physik 56 (1929), 330–352; original facsimile in Edition Open Sources](https://edition-open-sources.org/media/sources/10/14/sources10chap12.pdf)\n",
      "summary": "Weyl related position-dependent quantum phase freedom to a compensating electromagnetic potential in covariant differentiation. Simultaneous phase and potential changes preserve the proposed matter action, and the gauge-invariant action is connected with current conservation.\n\nA phase choice that varies from point to point changes how a wave field is differentiated. A corresponding potential change permits a covariant description. Weyl identifies the connection with electromagnetism and relates invariance to conservation within his specified action. This quantum unit-modulus phase construction differs from his earlier real-scale gauge proposal. The April PNAS sketch and the fuller May-received paper belong to one work family.",
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    "what_changed": "Local unit-modulus phase freedom is compensated by a potential transformation in covariant differentiation; the specified action connects gauge invariance with electromagnetic current conservation.",
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