Quantum field theory in a fractal universe (Calcagni)

[marcus]

At least one of us at this discussion board has expressed an interest in fractal modeling of spacetime, or of dynamics.*
This paper by Calcagni may be suggestive of what form such an approach could take.
http://arxiv.org/abs/1001.0571
Quantum field theory, gravity and cosmology in a fractal universe
Gianluca Calcagni
39 pages, 4 figures
(Submitted on 4 Jan 2010)
"We propose a model for a power-counting renormalizable field theory living in a fractal spacetime. The action is Lorentz covariant and equipped with a Stieltjes measure. The system flows, even in a classical sense, from an ultraviolet regime where spacetime has Hausdorff dimension 2 to an infrared limit coinciding with a standard D-dimensional field theory. We discuss the properties of a scalar field model at classical and quantum level. Classically, the field lives on a fractal which exchanges energy-momentum with the bulk of integer topological dimension D. Although an observer experiences dissipation, the total energy-momentum is conserved. The field spectrum is a continuum of massive modes. The gravitational sector and Einstein equations are discussed in detail, also on cosmological backgrounds. We find ultraviolet cosmological solutions and comment on their implications for the early universe."

Until recently Calcagni was at Ashtekar's Institute for Gravitation and the Cosmos (IGC) at Penn State. He has published papers in both string and LQG, as well as in other areas. In late 2009 he appears to have joined Hermann Nicolai's research outfit at Golm, the Albert Einstein Institute.

*Here is a related PF blog entry:
https://www.physicsforums.com/blog.php?b=1213

 

[Orbb]

It might be of interest that Calcagni recently compiled a shorter review of his approach, accepted for Phys. Rev. Lett.:
http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.3142v3.pdf

It is strongly related to and inspired by the scaling of the spectral dimension in various approaches, see e.g. the review by Carlip
http://arxiv.org/PS_cache/arxiv/pdf/0909/0909.3329v1.pdf.

or the case of NCG (not in the sense of Connes' approach):
http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.0220v3.pdf

Also it might be worthwile to remember the thread about Carlips paper,
https://www.physicsforums.com/showthread.php?t=323417.

I like his approach because he basically turns the logic of the above papers upside down to obtain new insights. The scaling dimension is likely to tell us something about the UV behaviour of gravity because it is a property shared by almost all approaches to QG.