Spectral dimension of a quantum universe
- Perimeter Institute for Theoretical Physics, 31 Caroline Street, Waterloo, ON N2L 2Y5 (Canada)
In this paper, we calculate in a transparent way the spectral dimension of a quantum spacetime, considering a diffusion process propagating on a fluctuating manifold. To describe the erratic path of the diffusion, we implement a minimal length by averaging the graininess of the quantum manifold in the flat space case. As a result we obtain that, for large diffusion times, the quantum spacetime behaves like a smooth differential manifold of discrete dimension. On the other hand, for smaller diffusion times, the spacetime looks like a fractal surface with a reduced effective dimension. For the specific case in which the diffusion time has the size of the minimal length, the spacetime turns out to have a spectral dimension equal to 2, suggesting a possible renormalizable character of gravity in this regime. For smaller diffusion times, the spectral dimension approaches zero, making any physical interpretation less reliable in this extreme regime. We extend our result to the presence of a background field and curvature. We show that in this case the spectral dimension has a more complicated relation with the diffusion time, and conclusions about the renormalizable character of gravity become less straightforward with respect to what we found with the flat space analysis.
- OSTI ID:
- 21409752
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 81, Issue 10; Other Information: DOI: 10.1103/PhysRevD.81.104040; (c) 2010 The American Physical Society; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Quantum field theory in non-integer dimensions
The fractal dimension of gravity data sets and its implication for gridding