Vacuum energy and renormalization of the field-independent term
Vacuum energy and renormalization of the field-independent term
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DOI：
10.1088/1475-7516/2022/03/062
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发表时间：
2021-06
影响因子：
6.4
通讯作者：
I. G. Márián;U. Jentschura;N. Defenu;A. Trombettoni;I. Nandori
中科院分区：
文献类型：
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作者：
I. G. Márián;U. Jentschura;N. Defenu;A. Trombettoni;I. Nandori
由于它的构造，非微扰重整化群（RG）演化的常数，场无关的条款（这是恒定的，但相对于场的变化取决于RG规模k）需要特别照顾内的功能重整化群（FRG）的方法。在某些情况下，势的常数项没有物理意义。然而，也有一些特殊情况，它收到了重要的申请。在低维（d = 1）中，在量子力学模型中，这项与非谐振子的基态能量有关。在更高维度（d = 4），它与爱因斯坦方程的Λ项相同，并且在宇宙暴胀中起作用。因此，在统计场论中，在平坦空间中，常数项可以与自由能相关联，而在弯曲空间中，它可以自然地与宇宙常数相关联。众所周知，为了得到基态能量的正确结果，必须对d = 1的量子非谐振子采用减法来去除RG流在其高能（UV）极限下出现的k 2项.需要进行减法，因为一旦包括常数项，RG流中就缺少高斯固定点。然而，如果高斯不动点在那里，则不需要进一步的减法。在这里，我们提出了一个减法k 4和k 2项的UV缩放的RG方程d = 4维，如果高斯不动点是失踪的RG流与常数项。最后，我们的结果的应用宇宙模型的评论。
Due to its construction, the nonperturbative renormalization group (RG) evolution of the constant, field-independent term (which is constant with respect to field variations but depends on the RG scale k) requires special care within the Functional Renormalization Group (FRG) approach. In several instances, the constant term of the potential has no physical meaning. However, there are special cases where it receives important applications. In low dimensions (d = 1), in a quantum mechanical model, this term is associated with the ground-state energy of the anharmonic oscillator. In higher dimensions (d = 4), it is identical to the Λ term of the Einstein equations and it plays a role in cosmic inflation. Thus, in statistical field theory, in flat space, the constant term could be associated with the free energy, while in curved space, it could be naturally associated with the cosmological constant. It is known that one has to use a subtraction method for the quantum anharmonic oscillator in d = 1 to remove the k 2 term that appears in the RG flow in its high-energy (UV) limit in order to recover the correct results for the ground-state energy. The subtraction is needed because the Gaussian fixed point is missing in the RG flow once the constant term is included. However, if the Gaussian fixed point is there, no further subtraction is required. Here, we propose a subtraction method for k 4 and k 2 terms of the UV scaling of the RG equations for d = 4 dimensions if the Gaussian fixed point is missing in the RG flow with the constant term. Finally, comments on the application of our results to cosmological models are provided.