Kinetic Factors in Affine Quantization and Their Role in Field Theory Monte Carlo

$\phi^{12}_3$的缩放仿射量子化是非平凡的

Scaled Affine Quantization of $φ^{12}_3$ is Nontrivial

该研究通过蒙特卡洛分析证明，r=12、n=3的协变欧几里得标量场论φ^r_n可通过缩放仿射量子化实现可接受的非平凡量子化，区别于正则量子化受渐近自由困扰的情况。

Scaled Affine Quantization of $φ^4_4$ in the Low Temperature Limit

We prove through Monte Carlo analysis that the covariant euclidean scalar field theory, $φ^r_n$, where $r$ denotes the power of the interaction term and $n = s + 1$ where $s$ is the spatial dimension and $1$ adds imaginary time, such that $r = n = 4$ can be acceptably quantized using scaled affine quantization and the resulting theory is nontrivial and renormalizable even at low temperatures in the highly quantum regime.

Monte Carlo evaluation of the continuum limit of the two-point function of two Euclidean Higgs real scalar fields subject to affine quantization

We study canonical and affine versions of the quantized covariant Euclidean Higgs scalar field-theory for two real fields on four dimensional lattices through the Monte Carlo method. We calculate the two-point function near the continuum limit at finite volume.

Monte Carlo evaluation of the continuum limit of the two-point function of the Euclidean free real scalar field subject to affine quantization

We study canonical and affine versions of the quantized covariant Euclidean free real scalar field-theory on four dimensional lattices through the Monte Carlo method. We calculate the two-point function at small values of the bare coupling constant and near the continuum limit at finite volume. Our investigation shows that affine quantization is able to give meaningful results for the two-point function for which is not available an exact analytic result and therefore numerical methods are necessary.

超局部 $φ^4_2$ 的标度仿射量子化：与正则量子化的路径积分蒙特卡洛比较研究

Scaled Affine Quantization of Ultralocal $φ^4_2$ a comparative Path Integral Monte Carlo study with Canonical Quantization

本研究通过路径积分蒙特卡洛方法，对比了超局部 $φ^4_2$ 模型在标度正则量子化与标度仿射量子化下的重整化性质，证明仿射量子化在 $r>2$ 时可得到非平庸理论。

标度仿射 φ₄⁴ 量子欧几里得协变相对论场论中格林函数的连续极限

Continuum limit of the Green function in scaled affine $φ^4_4$ quantum Euclidean covariant relativistic field theory

本文通过路径积分蒙特卡罗实验证明，标度仿射量子化方法使 φ₄⁴ 欧几里得协变相对论标量场论成为有效量子场论，其单点和两点函数具有良好定义的连续极限，并揭示了仅出现在量子层面的 ħ²/φ² 项。