The Mathematics of the AMEM Model: A Self-Contained Derivation Guide with Exercises
The Mathematics of the AMEM Model: A Self-Contained Derivation Guide with Exercises
A self-contained mathematics companion to 'Charge-Sign-Dependent Dark Gauge Coupling' (Kilgore 2026). Nine chapters covering every derivation in the primary preprint, with exercises and worked examples. Contents: (0) Notation and conventions; (1) Standard dark photon and kinetic mixing; (2) Construction of the C-odd current J^μ_C with proofs of C-oddness, CPT-evenness, and conservation; (3) AMEM Lagrangian — renormalizability and anomaly cancellation; (4) System-dependent coupling table; (5) Hydrogen vs. antihydrogen frequency shift derivation (factor-of-8 traced); (6) Both experimental constraint derivations (Baker 2025 and Van Dyck 1987) with full arithmetic; (7) UV completion mechanics; (8) N_eff cosmological bound; (9) Parameter space summary. Appendices: two worked numerical cross-checks, further reading, and complete symbol reference table.
Companion to the primary preprint (DOI: 10.5281/zenodo.19425223). Requires graduate-level quantum field theory background (equivalent to Peskin & Schroeder chapters 1-4).
dark photon phenomenology, CPT symmetry, exercises, gauge theory, dark photon, antimatter, pedagogical, beyond standard model, quantum field theory, C-violation, dark sector, constraint derivation
dark photon phenomenology, CPT symmetry, exercises, gauge theory, dark photon, antimatter, pedagogical, beyond standard model, quantum field theory, C-violation, dark sector, constraint derivation
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