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    "title": "Tomonaga: quantum states on spacelike surfaces",
    "summary": "The1943work, read through its1946English publication, reformulates quantum field-state evolution as a functional of a spacelike surface. Under the stated interaction-density and commutation assumptions, local surface deformations give an explicitly Lorentz-compatible formal description.\n\nDifferent observers disagree about which distant events happen at the same time. A field state tied only to one flat time slice can hide that issue. Tomonaga instead describes the state on a spacelike surface and how interactions change it when a small patch moves. This gives a way to express the same formal physics without privileging one observer’s time coordinate. The paper also states that this reformulation leaves the existing infinite quantities unresolved.",
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    "year": 1943,
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        "description": "Exact contribution is the 1943 formulation as represented by its 1946 English translation; Japanese original unread and no separate translation achievement. The argument assumes a scalar interaction-energy density and the required commutation at separated and adjacent spacelike points, motivated by the stated derivative-free interaction setting. Fields are transformed with free evolution; the surface-state equations are formal and restricted to spacelike surfaces, not arbitrary timelike boundaries. Section 4 handles continuum amplitudes through an indicated countable approximation and states results rather than supplying a modern measure-theoretic construction. Section 6 explicitly retains divergence problems and says the equations have pathological infinite solutions; this is not a renormalization proof, rigorous existence theorem for interacting continuum QFT or new verified physical prediction. equation images/glyphs imperfect, no independent reconstruction, replay or original-Japanese verification. Dirac/Bloch, Pauli, Stueckelberg, Heisenberg and Yukawa inputs remain inherited. Later Schwinger formulations, QED corrections and experimental confirmations are separate.",
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          "citation": "Tomonaga:1946 English publication of the1943 spacelike-surface field formulation",
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      "statement": "# Tomonaga: quantum states on spacelike surfaces\n\nThe1943work, read through its1946English publication, reformulates quantum field-state evolution as a functional of a spacelike surface. Under the stated interaction-density and commutation assumptions, local surface deformations give an explicitly Lorentz-compatible formal description.\n\nDifferent observers disagree about which distant events happen at the same time. A field state tied only to one flat time slice can hide that issue. Tomonaga instead describes the state on a spacelike surface and how interactions change it when a small patch moves. This gives a way to express the same formal physics without privileging one observer’s time coordinate. The paper also states that this reformulation leaves the existing infinite quantities unresolved.\n\n## Scientific scope\n\nExact contribution is the 1943 formulation as represented by its 1946 English translation; Japanese original unread and no separate translation achievement. The argument assumes a scalar interaction-energy density and the required commutation at separated and adjacent spacelike points, motivated by the stated derivative-free interaction setting. Fields are transformed with free evolution; the surface-state equations are formal and restricted to spacelike surfaces, not arbitrary timelike boundaries. Section 4 handles continuum amplitudes through an indicated countable approximation and states results rather than supplying a modern measure-theoretic construction. Section 6 explicitly retains divergence problems and says the equations have pathological infinite solutions; this is not a renormalization proof, rigorous existence theorem for interacting continuum QFT or new verified physical prediction. equation images/glyphs imperfect, no independent reconstruction, replay or original-Japanese verification. Dirac/Bloch, Pauli, Stueckelberg, Heisenberg and Yukawa inputs remain inherited. Later Schwinger formulations, QED corrections and experimental confirmations are separate.\n\n## People and systems\n\nS. Tomonaga\n\n\n\n## Original sources\n\n- [Tomonaga:1946 English publication of the1943 spacelike-surface field formulation](https://www.jstage.jst.go.jp/article/ptp1946/1/2/1_2_27/_pdf/-char/en)\n- [J-STAGE original publication metadata:Tomonaga1946translation](https://www.jstage.jst.go.jp/article/ptp1946/1/2/1_2_27/_article/-char/en)\n",
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      "title": "Tomonaga: quantum states on spacelike surfaces"
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    "title": "Tomonaga: quantum states on spacelike surfaces",
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