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arXiv 1012.3085gr-qchep-th
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弯曲偶维时空中的辐射反应

Radiation reaction in curved even-dimensional spacetime

Dmitri V. Gal'tsov, Pavel Spirin

摘要:

发展了一种计算弯曲时空中点粒子与无质量标量场和矢量场相互作用辐射反应的新方法。它是基于场格林函数的分析,两个点都位于粒子世界线上,不需要像DeWitt-Becomme方法那样在世界线之外积分场应力,从而大大简化了问题。我们从任意维的时空开始,证明了无质量标量和矢量格林函数的Hadamard展开式在偶数维中只包含Synge世界函数的整数逆幂,在奇数维中只包含半整数。偶数维的情况下,然后详细处理。我们分析发散,计算高导数的反项,并找到一个经常性的公式,在邻近的维度的反作用力的局部部分。高维弯曲空间反项并不简单地是平面反项的协变推广,而是包含了额外的曲率相关项。我们在四维和六维中说明我们的形式主义。在第一种情况下,我们以一种更简单的方式重新推导了DeWitt-Becomme-Hobbs的结果,在第二种情况下,我们给出了Kosyakov方程的协变推广。局部部分的反作用力被发现包含一项比例的黎曼张量,这是缺席的四维。

英文摘要:

We develop a new method of computing radiation reaction for a point particle interacting with massless scalar and vector fields in curved space-time. It is based on the analysis of field Green's functions with both points lying on the particle world-line and does not require integration of the field stresses outside the world line as was used in the DeWitt-Brehme approach, thus leading to a substantial simplification of the problem. We start with space-time of an arbitrary dimension and show that the Hadamard expansion of the massless scalar and vector Green's functions contain only integer inverse powers of the Synge world function in even dimensions and only half-integer in the odd dimensions. The even-dimensional case then is treated in detail. We analyze divergencies, calculate higher-derivative counterterms, and find a recurrent formula for the local parts of the reaction force in neighboring dimensions. Higher-dimensional curved space counterterms are not simply the covariant generalizations of the flat ones, but contain additional curvature-dependent terms. We illustrate our formalism in four and six dimensions. In the first case we rederive the results of DeWitt-Brehme-Hobbs in a simpler way, in the second case we give a covariant generalization of the Kosyakov equation. The local part of the reaction force is found to contain a term proportional to the Riemann tensor which is absent in four dimensions.

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