Grand Unified Polymerization Framework

This repository implements a comprehensive theoretical and computational framework for applying polymer quantization to Grand Unified Theories (GUTs). By extending the closed-form SU(2) recoupling machinery to unified gauge groups (SU(5), SO(10), E6), this framework enables simultaneous enhancement of quantum inequality violations across all charge sectors.

Recent Updates (June 2025)

🔄 Repository Reorganization Complete

• Fusion Code Migration: All polymer-induced-fusion code has been successfully migrated to the dedicated polymer-fusion-framework repository
• Focused Scope: This repository now exclusively focuses on fundamental GUT polymerization theory and mathematics
• Enhanced Integration: Maintains seamless integration with warp-bubble-optimizer for phenomenological applications

🚀 Latest Developments

• Platinum Road Deliverables: Complete implementation of platinum-road parameter validation and testing framework
• 3D Integration: Advanced 3D parameter space exploration with comprehensive validation
• QFT-ANEC Restoration: Restored and enhanced QFT averaged null energy condition framework
• Instanton Validation: Complete validation of polymer-modified instanton calculations with uncertainty quantification
• Enhanced Documentation: Comprehensive documentation updates and integration summaries

Key Features

• Unified Gauge Polymerization: Apply polymer quantization directly to GUT gauge fields rather than individual Standard Model sectors
• Hypergeometric Product Formulas: Closed-form expressions for SU(N) recoupling coefficients
• Multiplicative Enhancement: Coherently enhance electroweak, strong, and unified interactions with a single polymer parameter
• Running Coupling Analysis: Calculate unified coupling running with explicit β-function coefficients for SU(5), SO(10), and E6
• Non-perturbative Instanton Effects: Polymer-modified instanton rates with group-specific parameters
• Experimental Predictions: Quantitative predictions for proton decay, neutrino masses, and collider signatures

Mathematical Framework

The core mathematics extends our recent SU(2) closed-form generating functional work to unified groups:

G_G({x_e}) = ∫∏ᵥ d²ʳwᵥ/π^r e^(-∑ᵥ||wᵥ||²) ∏ₑ e^(xₑϵ_G(wᵢ,wⱼ)) = 1/√det(I - K_G({x_e}))

Where r is the rank of group G (r=4 for SU(5), r=5 for SO(10), r=6 for E6).

The polymerized unified propagator takes the form:

D̃ᵃᵇₘᵤᵥ(k) = δᵃᵇ × [ηₘᵤᵥ - kₘkᵥ/k²]/μ² × sinc²(μ√(k²+m²))

Where indices a,b run over the entire adjoint representation of the unified group.

The running coupling with polymer effects incorporated:

α_eff(E) = α₀/(1 - b_G/(2π)·α₀·ln(E/E₀))

Where b_G is the one-loop β-function coefficient specific to each GUT group.

The instanton rate with polymer modification:

Γ_inst^poly = Λ_G⁴ exp[-8π²/α_s(μ)·sin(μ·Φ_inst)/μ]

Where Λ_G is the characteristic scale of the gauge group and Φ_inst is the instanton topological charge.

Repository Structure

• unified_gut_polymerization/: Core implementation modules
  • core.py: Core numerical implementation with unified gauge polymerization
  • recoupling.py: Symbolic derivation of GUT recoupling coefficients
  • taylor_extraction.py: Taylor extraction to hypergeometric product mapping
  • running_coupling.py: Running coupling and instanton effects
  • parameter_scan.py: Advanced parameter space exploration
  • platinum_road_*.py: Platinum road deliverable implementations
  • restore_qft_anec_framework.py: QFT-ANEC framework restoration
• gut_unified_polymerization/: Alternative core implementation
  • core.py: Unified gauge polymerization with GUT group support
• docs/: Mathematical derivations and documentation
  • gut_polymer_core.tex: Mathematical derivations for GUT polymerization
  • taylor_extraction_su5.tex: Self-contained SU(5) Taylor extraction
  • unified_polymerized_feynman_rules.tex: Side-by-side comparison of classical vs polymerized Feynman rules
  • running_coupling_instantons.tex: Derivation of running coupling and instanton formulas with GUT constants
  • advanced_parameter_scan_visualization.tex: Advanced visualization techniques
  • high_resolution_parameter_scans.tex: High-resolution scanning methodologies
• examples/: Usage examples and demonstration scripts
  • demo_unified_gut_polymerization.py: Parameter scans and plots
  • advanced_lqg_integration.py: Integration with LQG code
  • symbolic_gut_recoupling.py: Demonstrates symbolic derivation
  • polymerized_feynman_rules_demo.py: Numerical demonstration of polymerized propagator and vertices
  • running_coupling_demo.py: Visualization of running coupling and instanton rates
  • high_resolution_parameter_scan.py: Advanced parameter scanning demonstration
• tests/: Validation and testing suite
• plan_a_step5_reactor_design/: Advanced reactor design analysis and validation

Connected Repositories

This repository is part of a connected ecosystem of theoretical physics research:

• warp-bubble-optimizer: Phenomenological applications and warp drive physics
• polymer-fusion-framework: Dedicated fusion research (migrated from this repo)

Installation

# Clone the repository
git clone https://github.com/arcticoder/unified-gut-polymerization.git

# Install dependencies
cd unified-gut-polymerization
pip install -e .

Usage Example

from unified_gut_polymerization import UnifiedGaugePolymerization, GUTConfig, RunningCouplingInstanton

# Configure a SU(5) GUT polymerization
config = GUTConfig(gut_group="SU(5)", mu_polymer=0.1)
gut_poly = UnifiedGaugePolymerization(config)

# Calculate cross-section enhancements
enhancements = gut_poly.unified_cross_section_enhancement(center_of_mass_energy=1000.0)
print(f"Total multiplicative enhancement: {enhancements['total_multiplicative']:.2e}x")

# Generate comprehensive enhancement plots
fig = gut_poly.plot_enhancement_spectra(save_path="enhancement_analysis.png")

# Running coupling and instanton calculations
rc_calculator = RunningCouplingInstanton(group="SU5")
coupling_at_1TeV = rc_calculator.running_coupling(energy=1e3)
instanton_rate = rc_calculator.instanton_rate(coupling=coupling_at_1TeV, mu=0.1)
print(f"SU(5) coupling at 1 TeV: {coupling_at_1TeV:.5f}")
print(f"Polymerized instanton rate: {instanton_rate:.2e}")

# Advanced parameter space exploration
from unified_gut_polymerization.parameter_scan import ParameterSpaceScan
scanner = ParameterSpaceScan(config)
results = scanner.platinum_road_scan()

Dependencies

• NumPy, SciPy, SymPy
• Matplotlib
• Unified-LQG package (for LQG integration)

Migration Notice

🔄 Repository Reorganization: All fusion-related code has been migrated to the dedicated polymer-fusion-framework repository as of June 2025. This repository now focuses exclusively on fundamental GUT polymerization theory.

References

• A. Arcticoder, "A Universal Generating Functional for SU(2) 3nj Symbols", May 24, 2025
• A. Arcticoder, "A Closed-Form Hypergeometric Product Formula for General SU(2) 3nj Recoupling Coefficients", May 25, 2025
• A. Arcticoder, "Closed-Form Matrix Elements for Arbitrary-Valence SU(2) Nodes via Generating Functionals", June 10, 2025