
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. Addendum for Ver. 7 (new attachment) Updated all four scattering notebooks (Compton, muon pair production, Møller, and Bhabha) to Ver. 7. The main improvement is the addition of AbsoluteTiming instrumentation, enabling systematic measurement of computation times for the 4×4 conventional, 256×256 Minkowski, and 256×256 curved-spacetime calculations. Benchmark results on a standard desktop PC (Intel Core i7-13700, 16 GB RAM): Compton scattering: 4×4: 4.3 s, 256×256 flat: 3,160 s (53 min), 256×256 curved: 9,697 s (2.7 h) Muon pair production: 4×4: 0.2 s, 256×256 flat: 1,153 s (19 min), 256×256 curved: 1,239 s (21 min) Møller scattering: 4×4: 7.9 s, 256×256 flat: 3,146 s (52 min), 256×256 curved: 5,921 s (1.6 h) Bhabha scattering: 4×4: 8.0 s, 256×256 flat: 2,703 s (45 min), 256×256 curved: 6,462 s (1.8 h) The 256×256 calculations require approximately 10²–10³ times longer than the conventional 4×4 calculations, owing to the increased matrix size (4² = 16 elements → 256² = 65,536 elements) and the expanded vertex loops (4² = 16 iterations → 16² = 256 iterations). Nevertheless, all tree-level processes complete within a few hours on a standard PC, confirming that the enlarged-matrix approach is computationally feasible for parameter scans and reproducibility checks.
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
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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