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ZENODO
Software . 2025
License: CC BY
Data sources: Datacite
ZENODO
Software . 2025
License: CC BY
Data sources: Datacite
ZENODO
Software . 2025
License: CC BY
Data sources: Datacite
ZENODO
Software . 2025
License: CC BY
Data sources: Datacite
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256×256 Gamma-Matrix QED Calculations: Compton, Muon-Pair Production, Møller, Bhabha

Authors: Maruyama, Hirokazu;

256×256 Gamma-Matrix QED Calculations: Compton, Muon-Pair Production, Møller, Bhabha

Abstract

We provide Mathematica notebooks and PDFs for four QED processes computed with a two index Gamma basis realized in a 256×256 representation. Version 6 revises the metric weighting so that $g^{\mu \nu} g_{\nu \sigma} = \delta^{\mu}_{\ \sigma}$ holds in code. In the flat limit the 256×256 results coincide with standard 4×4 outcomes. In curved spacetime, each scattering process can be evaluated using explicit local metric values,allowing numerical examination of deviations from the flat-space limit. This version enables direct construction of the effective Gamma operators with given local metric inputs,making the physical impact of curvature visible in computed observables. Addendum for Ver.6 (new attachment) • We include the verification notebook “05_gamma256_anticommutation_check Ver6”. It bulk-tests all 16x16 combinations of the two-index 256x256 basis (via determinant and related checks), confirming both the flat-space anticommutation of the 16 basis blocks and the metric-weighted mixed anticommutation: $$\begin{aligned}\Gamma_{\mu\nu}(x) &:= \Gamma_{\mu}{}^{\rho}\,g_{\rho\nu}(x),\\[2pt]\{\widehat{\Gamma}_{\mu}(x),\,\widehat{\Gamma}_{\nu}(x)\} &= 2\,g_{\mu\nu}(x)\,I_{256},\\[2pt]g^{\mu\nu}(x)\,g_{\nu\sigma}(x) &= \delta^{\mu}{}_{\sigma}.\end{aligned}$$ The script prints: “Gamma matrices … anticommutation relation confirmed OK” and “Mixed anticommutation relation OK”. • The tests use an explicit constant metric with off-diagonal entries (e.g.,$g_{02}=(1/10)^2$,$g_{23}=1/20)^2$, and scaled diagonals $g_{11}=g_{22}=g_{33}=(100/99)^2$), demonstrating that the matrix formalism remains consistent beyond diagonal metrics. Representative pairs reduce to “scalar × identity” for identical index pairs and to the zero matrix for different pairs, as expected. • Practically, Ver.6 constructs $\widehat{\Gamma}_{\nu}(x)$ directly from local metric inputs (no spin connection) and documents numeric checks that prevent spurious $g^2$ double counting in the algebra.

Keywords

Quantum Field Theory, Muon pair creation, Curved spacetime, 256×256 representation, High-Energy Physics, Barber (Bhabha) scattering, Quantum Electrodynamics, Mathematica notebooks, Dirac equation, Gamma matrices, Clifford algebra, Compton scattering, Particle Physics, Meller scattering

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average