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arXiv 1302.4486gr-qcastro-ph.COastro-ph.HEhep-phhep-th
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超相对论极限中的引力自作用力：“大N”展开

Gravitational self-force in the ultra-relativistic limit: The 'large-N' expansion

Chad R. Galley, Rafael A. Porto

备注：
12+23 pages, 24 figures. Paper substantially extended with more details on the formalism and computations. Submitted to JHEP
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摘要：

我们用有效场论方法研究了引力自作用力。我们证明了在超相对论极限γ \to \infty中，以γ为助推因子，许多简化产生了。与量子场论中的大N极限相对应，我们引入参数1/N = 1/γ^2，并证明有效作用量在1/N的每一阶上都有λ= Nε的幂次展开，其中ε= E_m/M，E_m=γm是小质量的动能.此外，我们还发现，具有非线性体相互作用的图首先进入O（λ^2/N^2），只有在世界线耦合中具有非线性的图才能在大N/超相对论极限中存活下来，这是非常容易计算的。最后，我们导出了O（λ^4/N）的自作用力，并给出了圆轨道的一些守恒量的表达式。

英文摘要：

We study the gravitational self-force using the effective field theory formalism. We show that in the ultra-relativistic limit γ\to \infty, with γthe boost factor, many simplifications arise. Drawing parallels with the large N limit in quantum field theory, we introduce the parameter 1/N = 1/γ^2 and show that the effective action admits a well defined expansion in powers of λ= Nε, at each order in 1/N, where ε= E_m/M and E_m=γm is the (kinetic) energy of the small mass. Moreover, we show that diagrams with nonlinear bulk interactions first enter at O(λ^2/N^2) and only diagrams with nonlinearities in the worldline couplings, which are significantly easier to compute, survive in the large N/ultra-relativistic limit. Finally, we derive the self-force to O(λ^4/N) and provide expressions for some conservative quantities for circular orbits.

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