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Radiation back-reaction and renormalization in classical field theory with singular sources

机译：具有奇异源的经典场论中的辐射后反应和再归一化

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摘要

We propose a general covariant method for regularizing the radiation back-reaction in linear and nonlinear field theory models with singular sources. Typical examples of such sources are the currents produced by extended relativistic objects (branes). As an illustration, we consider the models of minimal and nonminimal coupling of a brane to an n-form gauge field, a scalar field, and the Einstein gravity field. We find the structure of divergent and finite contributions due to the radiation back-reaction and obtain relations for the parameters of the theory ensuring cancellation of divergences. We prove that the divergences are Lagrangian in the case where the metric induced on the brane surface is nondegenerate. We find special types of a (nonminimal) coupling leading to local and Lagrangian effective equations of motion of the brane. We show that the requirement for classical renormalizability imposes strong restrictions on the self-coupling vertices of the held, similar to the quantum renormalizability conditions. In particular, we establish the nonrenormalizability of the gravitational self-coupling of a codimension-(k > 2) brane, whereas for k <= 2, the theory becomes not only renormalizable but also finite.
机译：我们提出了一种通用协变方法，用于对带有奇异源的线性和非线性场论模型中的辐射反作用进行正则化。这种来源的典型示例是扩展的相对论物体（大脑）产生的电流。作为说明，我们考虑将麸皮与n型规范场，标量场和爱因斯坦重力场的最小和非最小耦合模型。我们找到了由于辐射背反应而产生的发散和有限贡献的结构，并获得了确保消散的理论参数关系。我们证明了在麸面诱导的度量不退化的情况下，散度是拉格朗日。我们发现（非最小）耦合的特殊类型导致了局部和拉格朗日有效的运动方程。我们表明，对经典可重归化性的要求对所持有的自耦合顶点施加了严格的限制，类似于量子可重归化性条件。特别是，我们建立了余量-（k> 2）膜的重力自耦合的不可重归一化性，而对于k <= 2，该理论不仅可重归一化，而且变得有限。

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