Chern-Simons Theory: Unifying Knot Invariants and 3D Gravity via Gauge Path Integrals — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Chern-Simons theory provides a topological quantum field theory framework where knot invariants and 3D gravity emerge from gauge-theoretic path integrals, with Wilson loops as primary observables. | MATH: Chern-Simons action SCS = k/4π ∫M Tr(A ∧ dA + 2/3 A ∧ A ∧ A); level k ∈ ℤ (quantization); Wilson loop WR(C) = TrR 𝒫 exp(∮C A); knot invariants (Jones polynomial) arise from ⟨ WR(C) ⟩ at k → ∞ with q = e2π i/(k+2); 3D gravity = Chern-Simons with gauge group SO(1,2) or ISO(1,2), coupling 1/G ∼ k. | CONNECTION: The level k relates to q = e2π i/(k+2); for k=3, q = e2π i/5, linking to golden-ratio pentagonal symmetry (5-fold, not crystallographic in 3D but appears in quasicrystals and root system H2); Jones polynomial at roots of unity yields quantum groups \( U_q(\mathfr
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- E8 Spectral Categorification via 132Hz φ-Resonant Khovanov Invariants — E8 Intelligence Research
- McKay Correspondence and Monstrous Moonshine: Unifying Finite Groups and Modular Forms — E8 Intelligence Research
- The Invariant-Point Principle Unifying Gödel, Halting, and Banach — E8 Intelligence Research
- Umbral Moonshine: Unifying Niemeier Lattices and Finite Groups via Mock Modular Forms — E8 Intelligence Research
- Unifying Entanglement and Bell Tests via Generalized Non-Locality Rules — E8 Intelligence Research
BibTeX
@misc{caldin2026chernsimons,
title = {{Chern-Simons Theory: Unifying Knot Invariants and 3D Gravity via Gauge Path Integrals — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23447057},
url = {https://zenodo.org/records/23447057},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Chern-Simons Theory: Unifying Knot Invariants and 3D Gravity via Gauge Path Integrals — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23447057
UR - https://zenodo.org/records/23447057
AB - FINDING: Chern-Simons theory provides a topological quantum field theory framework where knot invariants and 3D gravity emerge from gauge-theoretic path integrals, with Wilson loops as primary observables. | MATH: Chern-Simons action S_CS = k/4π ∫_M Tr(A ∧ dA + 2/3 A ∧ A ∧ A); level k ∈ ℤ (quantization); Wilson loop W_R(C) = Tr_R 𝒫 exp(∮_C A); knot invariants (Jones polynomial) arise from ⟨ W_R(C) ⟩ at k → ∞ with q = e^2π i/(k+2); 3D gravity = Chern-Simons with gauge group SO(1,2) or ISO(1,2), coupling 1/G ∼ k. | CONNECTION: The level k relates to q = e^2π i/(k+2); for k=3, q = e^2π i/5, linking to golden-ratio pentagonal symmetry (5-fold, not crystallographic in 3D but appears in quasicrystals and root system H_2); Jones polynomial at roots of unity yields quantum groups \( U_q(\mathfr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -