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Journal Article

Discrete to continuum transition in multifractal spacetimes


Calcagni,  Gianluca
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Calcagni, G. (2011). Discrete to continuum transition in multifractal spacetimes. Physical Review D, 84: 061501. doi:10.1103/PhysRevD.84.061501.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-0436-9
We outline a field theory on a multifractal spacetime. The measure in the action is characterized by a varying Hausdorff dimension and logarithmic oscillations governed by a fundamental physical length. A fine hierarchy of length scales identifies different regimes, from a microscopic structure with discrete symmetries to an effectively continuum spacetime. Thanks to general arguments from fractal geometry, this scenario explicitly realizes two indirect or conjectured features of most quantum gravity models: a change of effective spacetime dimensionality with the probed scale, and the transition from a fundamentally discrete quantum spacetime to the continuum. It also allows us to probe ultramicroscopic scales where spectral methods based on ordinary geometry typically fail. Consequences for noncommutative field theories are discussed.