dorsal/arxiv
View SchemaA Map from Scalar Field Theory to Integer Polynomial Solutions
| Authors | Gordon Chalmers |
|---|---|
| Categories | |
| ArXiv ID | physics/0506013 |
| URL | https://arxiv.org/abs/physics/0506013 |
Abstract
The terms in the quantum scattering in scalar field theory models is parameterized by the invariants $\prod s_{ij}^{n_{ij}}$. The $s_{ij}$ are kinematic two-particle invariants, and the $n_{ij}$ are integers. The coefficients of these terms are computed via integrating all Feynman diagrams, or within the derivative expansion by solving the iteration equations. The latter has been provided recently; the functions which are prefactors of the individual terms $\prod s_{ij}^{n_{ij}}$ can be interpreted as terms in the expansions of L-series, which may be specified by collections of their zeroes. Once finding the appropriate elliptic curve coefficients, these quantum field solutions provide an algorithm to determining all of the mod p zeros to the algebraic curves. The latter is presumably determined by 'experimental' computer modeling or by the appropriate determination of the quantum prefactors.
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"date_created": "2026-03-02T18:01:00.714000Z",
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"abstract": "The terms in the quantum scattering in scalar field theory models is\nparameterized by the invariants $\\prod s_{ij}^{n_{ij}}$. The $s_{ij}$ are\nkinematic two-particle invariants, and the $n_{ij}$ are integers. The\ncoefficients of these terms are computed via integrating all Feynman diagrams,\nor within the derivative expansion by solving the iteration equations. The\nlatter has been provided recently; the functions which are prefactors of the\nindividual terms $\\prod s_{ij}^{n_{ij}}$ can be interpreted as terms in the\nexpansions of L-series, which may be specified by collections of their zeroes.\nOnce finding the appropriate elliptic curve coefficients, these quantum field\nsolutions provide an algorithm to determining all of the mod p zeros to the\nalgebraic curves. The latter is presumably determined by \u0027experimental\u0027\ncomputer modeling or by the appropriate determination of the quantum\nprefactors.",
"arxiv_id": "physics/0506013",
"authors": [
"Gordon Chalmers"
],
"categories": [
"physics.gen-ph"
],
"title": "A Map from Scalar Field Theory to Integer Polynomial Solutions",
"url": "https://arxiv.org/abs/physics/0506013"
},
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"type": "Model",
"variant": "snapshot-2026-03-01",
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