Sine-Gordon Universality Across Physical Systems: A Pedagogical Review — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Sine-Gordon model appears across superconductors, spin ladders, pendulums, and integrable defects — but the search results are pedagogical/demonstrative, not a specific new research breakthrough on zigzag ladders with unequal exchange. | MATH: Core equation: utt − uxx + sin u = 0 (1+1D sine-Gordon). Bosonization maps spinful Tomonaga-Luttinger liquid to sine-Gordon with coupling g ∝ cos(√2ϕ) for backscattering; spin-charge separation yields charge boson ϕc and spin boson ϕs, with zigzag ladder frustration producing a gap via cos(√8ϕs) terms. Defect construction uses quantum affine sl2 representations (q-oscillators), generalising Q-operators. | CONNECTION: The sine-Gordon potential cos u has period 2π — a root-system periodicity of A1. Soliton/kink solutions interpolate between vacua u=0 and u=2π, with kink mass M = 8√λ (for λ=1). Breather frequency \(\omega =
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026sinegordon,
title = {{Sine-Gordon Universality Across Physical Systems: A Pedagogical Review — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23587048},
url = {https://zenodo.org/records/23587048},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sine-Gordon Universality Across Physical Systems: A Pedagogical Review — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23587048
UR - https://zenodo.org/records/23587048
AB - FINDING: Sine-Gordon model appears across superconductors, spin ladders, pendulums, and integrable defects — but the search results are pedagogical/demonstrative, not a specific new research breakthrough on zigzag ladders with unequal exchange. | MATH: Core equation: u_tt − u_xx + sin u = 0 (1+1D sine-Gordon). Bosonization maps spinful Tomonaga-Luttinger liquid to sine-Gordon with coupling g ∝ cos(√2ϕ) for backscattering; spin-charge separation yields charge boson ϕ_c and spin boson ϕ_s, with zigzag ladder frustration producing a gap via cos(√8ϕ_s) terms. Defect construction uses quantum affine sl_2 representations (q-oscillators), generalising Q-operators. | CONNECTION: The sine-Gordon potential cos u has period 2π — a root-system periodicity of A_1. Soliton/kink solutions interpolate between vacua u=0 and u=2π, with kink mass M = 8√λ (for λ=1). Breather frequency \(\omega = Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -