Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1, D-14476 Golm, Germany.
Phys Rev Lett. 2010 Jun 25;104(25):251301. doi: 10.1103/PhysRevLett.104.251301. Epub 2010 Jun 24.
We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.
我们提出了一种在分形时空中存在的场论，该场论被认为是洛伦兹不变的、可重正化的、紫外有限的和因果的。该系统从一个紫外固定点流动，在那里时空具有豪斯多夫维数 2，到一个与标准四维场论一致的红外极限。经典地，场所在的分形世界与具有整数拓扑维数的体交换能量动量。然而，总能量动量是守恒的。我们考虑标量场的动力学和传播子。讨论了对量子引力、宇宙学和宇宙常数的影响。
