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 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.

中文翻译：

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仿射量化欧几里得自由实标量场两点函数连续统极限的蒙特卡罗评价

我们通过蒙特卡罗方法研究四维格子上量化协变欧几里得自由实标量场理论的规范和仿射版本。我们计算了有限体积下连续介质极限附近的两点函数。我们的研究表明，仿射量化能够为无法获得精确解析结果的两点函数提供有意义的结果，因此需要数值方法。