arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 1001.0571hep-thastro-ph.COgr-qc
收藏

分形宇宙中的量子场论、引力和宇宙学

Quantum field theory, gravity and cosmology in a fractal universe

Gianluca Calcagni

摘要:

我们提出了一个生活在分形时空中的功率计数可重整化场论模型。该行动是洛伦兹协变的,并配备了斯蒂尔捷斯措施。即使在经典意义上,这个系统也是从时空的豪斯多夫维数为2的紫外区流动到符合标准$D$维场论的红外区。讨论了标量场模型在经典和量子水平上的性质。经典地,场存在于与整数拓扑维数D的大部分交换能量-动量的分形上。虽然观察者经历耗散,但总的能量动量是守恒的。场谱是大量模的连续谱。详细讨论了引力扇区和爱因斯坦方程,也讨论了宇宙学背景。我们发现紫外宇宙学的解决方案,并评论其对早期宇宙的影响。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑