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    "summary": "Fock connected changes of electromagnetic potentials with a compensating phase factor in the charged scalar wavefunction. An additional coordinate parameter made the combined transformation explicit in his invariant wave-equation representation.\n\nFock changes the vector/scalar potentials by derivatives of an arbitrary function and compensates with a shift of the extra coordinate. Exponential dependence on that coordinate becomes a unit-modulus phase factor for the wavefunction. His note in proof explicitly acknowledges Klein’s independently obtained results as identical in principle. Weyl’s later spinor and local-phase field organization is a related, distinct contribution.",
    "boundary": "The target is the 1926 potential/phase relation within the stated scalar-wave and extra-coordinate ansatz. Stationary energy-level discussion uses time-independent coefficients and suitable finiteness/continuity requirements; it is not invariance of every energy label under arbitrary time-dependent gauges. No full modern gauge-field theory, Dirac-spinor extension, physical extra-dimension evidence, independent certification of translated equations or exclusive priority is claimed.",
    "area": "Wave-equation gauge covariance",
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    "year": 1926,
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            "citation": "V. Fock, Über die invariante Form der Wellen- und der Bewegungsgleichungen für einen geladenen Massenpunkt (1926), English translation in Selected Works (CRC2004),pp.21–28",
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      "scope": {
        "description": "The target is the 1926 potential/phase relation within the stated scalar-wave and extra-coordinate ansatz. Stationary energy-level discussion uses time-independent coefficients and suitable finiteness/continuity requirements; it is not invariance of every energy label under arbitrary time-dependent gauges. No full modern gauge-field theory, Dirac-spinor extension, physical extra-dimension evidence, independent certification of translated equations or exclusive priority is claimed.",
        "domain": "Wave-equation gauge covariance"
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      "sources": [
        {
          "citation": "V. Fock, Über die invariante Form der Wellen- und der Bewegungsgleichungen für einen geladenen Massenpunkt (1926), English translation in Selected Works (CRC2004),pp.21–28",
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      "statement": "# Fock: electromagnetic-potential changes and wavefunction phase\n\nFock connected changes of electromagnetic potentials with a compensating phase factor in the charged scalar wavefunction. An additional coordinate parameter made the combined transformation explicit in his invariant wave-equation representation.\n\nFock changes the vector/scalar potentials by derivatives of an arbitrary function and compensates with a shift of the extra coordinate. Exponential dependence on that coordinate becomes a unit-modulus phase factor for the wavefunction. His note in proof explicitly acknowledges Klein’s independently obtained results as identical in principle. Weyl’s later spinor and local-phase field organization is a related, distinct contribution.\n\n## Scientific scope\n\nThe target is the 1926 potential/phase relation within the stated scalar-wave and extra-coordinate ansatz. Stationary energy-level discussion uses time-independent coefficients and suitable finiteness/continuity requirements; it is not invariance of every energy label under arbitrary time-dependent gauges. No full modern gauge-field theory, Dirac-spinor extension, physical extra-dimension evidence, independent certification of translated equations or exclusive priority is claimed.\n\n## People and systems\n\nVladimir Aleksandrovich Fock\n\n\n\n## Original sources\n\n- [V. Fock, Über die invariante Form der Wellen- und der Bewegungsgleichungen für einen geladenen Massenpunkt (1926), English translation in Selected Works (CRC2004),pp.21–28](https://api.pageplace.de/preview/DT0400.9781134422005_A38205403/preview-9781134422005_A38205403.pdf)\n",
      "summary": "Fock connected changes of electromagnetic potentials with a compensating phase factor in the charged scalar wavefunction. An additional coordinate parameter made the combined transformation explicit in his invariant wave-equation representation.\n\nFock changes the vector/scalar potentials by derivatives of an arbitrary function and compensates with a shift of the extra coordinate. Exponential dependence on that coordinate becomes a unit-modulus phase factor for the wavefunction. His note in proof explicitly acknowledges Klein’s independently obtained results as identical in principle. Weyl’s later spinor and local-phase field organization is a related, distinct contribution.",
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    "title": "Fock: electromagnetic-potential changes and wavefunction phase",
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    "what_changed": "The extra-coordinate transformation exposes a compensating unit-modulus scalar-wavefunction phase under changes of electromagnetic potentials in the stated representation.",
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    "references": [
      {
        "title": "V. Fock, Über die invariante Form der Wellen- und der Bewegungsgleichungen für einen geladenen Massenpunkt (1926), English translation in Selected Works (CRC 2004), pp.21–28",
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