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

• URL: http://arxiv.org/abs/2109.13447v4
• Date: Mon, 5 Dec 2022 18:17:55 GMT
• Title: Scaled Affine Quantization of Ultralocal $\varphi^4_2$ a comparative Path Integral Monte Carlo study with Canonical Quantization
• Authors: Riccardo Fantoni and John R. Klauder
• Abstract summary: We show that $r geq 2n/(n-2) can be acceptably quantized and the resulting theory is nontrivial, unlike what happens using canonical quantization. In particular we consider the ultralocal $varphi4$ model and its renormalized properties for both the scaled canonical quantization and the scaled affine quantization version.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: After the success of affine quantization in proving through Monte Carlo analysis that the covariant euclidean scalar field theory, $\varphi^r_n$, 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 $\varphi^4_2$ model and study its renormalized properties for both the scaled canonical quantization version and the scaled affine quantization version through path integral Monte Carlo.

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