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Fractal Geometry of Higher Derivative Gravity
Maximilian Becker1, Carlo Pagani1,2, Omar Zanusso3
1Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, D-55099 Mainz, Germany.
Physical Review Letters
|May 2, 2020
Summary
We explored how geometric properties like length and area scale in quantum gravity models. Our findings reveal the fractal dimensions of spacetime at microscopic scales.
Area of Science:
- Theoretical Physics
- Quantum Gravity
- Geometric Measure Theory
Background:
- Understanding the behavior of geometric quantities at the Planck scale is crucial for a complete theory of quantum gravity.
- Previous models have faced challenges in consistently defining and renormalizing geometric operators.
Purpose of the Study:
- To determine the scaling properties of geometric operators in higher derivative quantum gravity.
- To investigate the fractal nature of spacetime at very small distances.
Main Methods:
- Renormalization of composite operators.
- Analysis of scaling properties of lengths, areas, and volumes.
- Deduction of fractal dimensions.
Main Results:
- Established the scaling laws for geometric operators in higher derivative quantum gravity models.
- Quantified the fractal dimensions of hypersurfaces within quantum spacetime.
- Demonstrated a consistent renormalization procedure for composite operators.
Conclusions:
- The study provides insights into the geometric structure of quantum spacetime at the smallest scales.
- The results have implications for understanding emergent spacetime and quantum geometry.
- The renormalization technique offers a robust method for analyzing quantum gravity models.
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