Matter Quantum Corrections to the Graviton Self-Energy and the Newtonian Potential
Matter Quantum Corrections to the Graviton Self-Energy and the Newtonian Potential
复制标题
对引力子自能和牛顿势的物质量子修正
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Pilaftsis
中科院分区：
文献类型：
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作者：
Daniel Burns;A. Pilaftsis
我们重新研究了平闵可夫斯基背景下物质量子效应对引力子自能的影响，以期对引力子无质量的机制有更深入的了解。为此，我们导出了一个低能定理，它直接将宇宙常数的辐射修正与引力子质量的辐射修正与微扰理论中所有阶的辐射修正联系起来。作为一个说明性的例子，我们考虑了一个与引力最小耦合的阿贝尔希格斯模型，并明确地展示了宇宙常数的适当重正化如何导致引力子质量在单环水平上消失。在相同的阿贝尔希格斯模型中，我们还计算了牛顿势的物质量子修正，并根据环中粒子质量的修正贝塞尔和斯特鲁夫函数给出了解析公式。我们表明，一旦仔细考虑非零环质量的非相对论性极限，对牛顿势的修正就会表现出对距离r的指数衰减依赖。对于环中的无质量标量、费米子和规范玻色子，我们恢复了文献中提出的众所周知的结果。
We revisit the calculation of matter quantum effects on the graviton self-energy on a flat Minkowski background, with the aim to acquire a deeper understanding of the mechanism that renders the graviton massless. To this end, we derive a low-energy theorem which directly relates the radiative corrections of the cosmological constant to those of the graviton mass to all orders in perturbation theory. As an illustrative example, we consider an Abelian Higgs model with minimal coupling to gravity and show explicitly how a suitable renormalization of the cosmological constant leads to the vanishing of the graviton mass at the one-loop level. In the same Abelian Higgs model, we also calculate the matter quantum corrections to the Newtonian potential and present analytical formulas in terms of modified Bessel and Struve functions of the particle masses in the loop. We show that the correction to the Newtonian potential exhibits an exponential fall-off dependence on the distance r, once the nonrelativistic limit with respect to the nonzero loop mass is carefully considered. For massless scalars, fermions, and gauge bosons in the loops, we recover the well-known results presented in the literature.