Scalar Field Theory and Zero-Point Energy Coupling
Mathematical preliminaries, Klein-Gordon formulation, quantum vacuum physics, Casimir effect, and parametric resonance mechanisms for field-vacuum coupling.
Download PDFResearch Papers
PhysicsForge presents a comprehensive theoretical framework synthesizing multiple approaches to fundamental physics. Each paper employs the Lions Commentary pedagogical style with extensive marginal annotations, dimensional analysis, worked numerical examples, and publication-quality TikZ/PGFPlots visualizations.
Exceptional Lie Algebras and Crystalline Lattice Structures
Cayley-Dickson construction, E8/E7/E6/F4/G2 Lie groups, crystalline spacetime engineering, and modular moonshine connections.
Download PDFFractal Geometry and Hyperdimensional Field Structures
Fractal calculus, Hausdorff dimension, Kaluza-Klein compactification, AdS/CFT correspondence, and renormalization group flows.
Download PDFGravitational-Electromagnetic Unification via Scalar Intermediaries
Historical context, Brans-Dicke scalar-tensor gravity, Maxwell equations in curved spacetime, EM-gravity coupling, and unified field equations.
Download PDFExperimental Protocols for Exotic Quantum States
Discrete time crystals, quantum foam phenomenology, holographic entropy measurements, scalar field detection, and dimensional spectroscopy.
Download PDFApplications to Quantum Computing and Energy Technologies
Topological quantum computing with E8 anyons, zero-point energy extraction, metamaterial spacetime engineering, and future technology roadmap.
Download PDFKey Features
📚 Lions Commentary Style
8 types of marginal notes providing physics intuition, historical context, computational tips, and cross-references.
📐 Dimensional Analysis
Every equation annotated with units and typical values. Complete dimensional checks throughout.
🎨 100+ Visualizations
Publication-quality TikZ diagrams and PGFPlots embedded directly in LaTeX.
🧮 Worked Examples
50+ numerical examples with complete derivations. Every result demonstrated computationally.
Mathematical Framework
The framework is built on rigorous mathematical foundations. Key equations include:
$\Box \phi + V'(\phi) + \xi R \phi = 0$
Scalar Field Equation in Curved Spacetime (Paper 1)
$F_{\text{Casimir}} = -\frac{\pi^2 \hbar c}{240 d^4}$
Casimir Force Between Parallel Plates (Papers 1, 5)
$\text{dim}(\text{E}_8) = 248$
E8 Lie Algebra — Candidate for Deepest Symmetry (Paper 2)
$G_{\mu\nu} + \alpha F_{\mu\alpha}F_\nu^{\ \alpha} = 8\pi G\, T_{\mu\nu}$
EM-Gravity Coupled Field Equations (Paper 4)
Theoretical Synthesis
PhysicsForge synthesizes multiple approaches to fundamental physics:
- Scalar Field Dynamics: Zero-point energy coupling, quantum vacuum fluctuations, Casimir effect
- Exceptional Symmetries: E8, E7, E6, F4, G2 Lie groups and Cayley-Dickson algebras
- GEM Formalism: Gravitoelectromagnetic unification with scalar-vacuum interactions
- Fractal Geometry: Hausdorff dimension, renormalization group flows, holographic principle
- Experimental Protocols: Time crystals, quantum foam, holographic entropy, spectral dimension
- Applications: Topological quantum computing, metamaterials, energy technologies
Repository Structure
The complete LaTeX source code, Python analysis tools, and build system are available:
synthesis/papers/— 6 modular research papers (26 chapters total)synthesis/shared/— Shared LaTeX infrastructure (preamble, macros, glossary)modules/equations/— 246+ modular equation filesscripts/— Python tools for equation extraction and analysisfigures/tikz/— TikZ/PGFPlots visualizations
License and Credits
This work is licensed under the GNU General Public License v3.0.
Credits:
- Lions Commentary pedagogical style inspired by John Lions' Unix V6 commentary
- Multiple LLMs including Claude (Anthropic), ChatGPT (OpenAI), and others
- Open-source contributors and researchers
See the LICENSE file for full details.