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arXiv 2109.09753hep-thgr-qc
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用不变观测量对牛顿势的引力子修正

Graviton corrections to the Newtonian potential using invariant observables

M. B. Fröb, C. Rein, R. Verch

摘要:

我们考虑耦合到一个点粒子的微扰量子引力的有效理论,在平坦空间中量子化引力场和粒子位置的涨落。使用最近的关系的方法来构建规范不变的可观测量,我们计算一圈引力子修正不变的度规扰动,其时间-时间分量给出了牛顿引力势。由此产生的量子修正由两部分组成:第一部分源于引力子环,与其他方法得出的修正一致,而第二部分源于粒子位置和能量动量的量子涨落,可以被视为“Zitterbewegung”的模拟。作为对计算的检查,我们还恢复了经典的修正,这与史瓦西度规的微扰展开一致。

英文摘要:

We consider the effective theory of perturbative quantum gravity coupled to a point particle, quantizing fluctuations of both the gravitational field and the particle's position around flat space. Using a recent relational approach to construct gauge-invariant observables, we compute one-loop graviton corrections to the invariant metric perturbation, whose time-time component gives the Newtonian gravitational potential. The resulting quantum correction consists of two parts: the first stems from graviton loops and agrees with the correction derived by other methods, while the second one is sourced by the quantum fluctuations of the particle's position and energy-momentum, and may be viewed as an analog of a "Zitterbewegung". As a check on the computation, we also recover classical corrections which agree with the perturbative expansion of the Schwarzschild metric.

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