论文标题
缩放对应机制
Scaling-correspondence mechanism
论文作者
论文摘要
1970年代，威尔逊展示了有效拉格朗日人的重新归一化和缩放的深厚联系。 Polchinski进一步证明了这种联系暗示着扰动场理论的可误差。我们通过扩展有效拉格朗日的缩放转换来开发机制 - 在低能量有效磁场理论（EFT）的量子场与其尺度相应（裸露的）模型之间引入了田间图。我们通过真实标量$ ϕ^4 $模型研究机制。我们发现，如果EFT的潜力从EFT的潜力中订单$ n $的自我交流，则（最多）$ n-1 $缩放量表可与EFT相同的对称组相对应。然后，我们通过将机制应用于通货膨胀范式来研究宇宙学的潜在应用。我们发现生成的通货膨胀模型（来自实际标量$ ϕ^4 $ eft）是幂律通货膨胀模型。我们简要检查产生的通货膨胀模型的一致性与通货膨胀的典型观察限制 - 光谱指数（$ n_ {s} $），e -folds和张量/标量比（$ r $）。
In 1970s, Wilson shown the deep connection of renormalization and scaling of the effective Lagrangian. Polchinski further proved that such connection implied renormalizability of perturbative field theory. We develop the mechanism by an extension of scaling transformation of the effective Lagrangian - introducing a field-map between the quantum fields of the low-energy effective field theory (EFT) and its' scaling-corresponding (bare) model. We study the mechanism through real scalar $ϕ^4$ model. We found if there is a self-interaction of order $N$ from the EFT's potential, there are (at most) $N-1$ scaling-corresponding models for the same symmetry group of the EFT. We then study the potential application for cosmology by applying the mechanism to inflation paradigm. We found the generated inflation model (from the real scalar $ϕ^4$ EFT) is the power-law inflation model. We briefly check the consistency of the generated inflation model against the inflation's typical observational constraints - spectral index ($n_{s}$), e-folds, and tensor/scalar ratio ($r$).
