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arXiv 1210.0507hep-thgr-qc
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有效量子引力背景下的相互作用标量场

Interacting Scalar Fields in the Context of Effective Quantum Gravity

Artur R. Pietrykowski

摘要:

具有四次和更高幂次相互作用的四维标量场理论在量子水平上存在平凡性问题。这是由于耦合常数,与物理预期相反,似乎没有能量约束的增长。由于这个问题涉及到高能领域,与量子引力场的相互作用可以提供自然的解决方案,本文考虑了具有一般解析势的标量场理论,该势具有$\mathbb{Z}_2$对称性并与量子引力场相互作用.后者的动力学由宇宙学常数和爱因斯坦-希尔伯特项控制,它们都是量子引力有效理论的最低项和次低项。利用Vilkovisky-DeWitt方法计算了对标量场有效作用量的单圈修正。我们还导出了MS方案中所有标量场耦合的唯一单圈β函数。我们发现,主导引力修正作用在渐近自由的方向上。此外,假设两个常数的牛顿和宇宙有非零的不动点值,我们发现渐近自由Halpern-Huang潜力。

英文摘要:

A four dimensional scalar field theory with quartic and of higher power interactions suffers the triviality issue at the quantum level. This is due to coupling constants that, contrary to the physical expectations, seem to grow without a bound with energy. Since this problem concerns the high energy domain, interaction with a quantum gravitational field may provide natural solution to it. In this paper we address this problem considering a scalar field theory with a general analytic potential having $\mathbb{Z}_2$ symmetry and interacting with a quantum gravitational field. The dynamics of the latter is governed by the cosmological constant and the Einstein-Hilbert term both being the lowest and next-to-the lowest terms of the effective theory of quantum gravity. Using the Vilkovisky-DeWitt method we calculate the one loop correction to the scalar field effective action. We also derive the unique one loop beta functions for all the scalar field couplings in the MS scheme. We find that the leading gravitational corrections act in the direction of asymptotic freedom. Moreover, assuming for both constants the Newton and the cosmological to have non-zero fixed point values we find asymptotically free Halpern-Huang potentials.

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