Scaled Affine Quantization of Ultralocal $φ^4_2$ a comparative Path Integral Monte Carlo study with Canonical Quantization
Riccardo Fantoni, John R. Klauder · arXiv (Cornell University) · 2021
After the success of affine quantization in proving through Monte Carlo analysis that the covariant euclidean scalar field theory, $φ^r_n$, where $r$ denotes the power of the interaction term and $n = s + 1$ with $s$ the spatial dimension and $1$ adds imaginary time, such that $r \geq 2n/(n-2)$ can be acceptably quantized and the resulting theory is nontrivial, unlike what happens using canonical quantization, we show here that the same has to be expected for $r>2$ and any $n$ even for the ultralocal field theory. In particular we consider the ultralocal $φ^4_2$ model and study its renormalized properties for both the scaled canonical quantization version and the scaled affine quantization version through path integral Monte Carlo.