Using Affine Quantization to Analyze Non-renormalizable Scalar Fields and the Quantization of Einstein's Gravity

TL;DR

This paper explores affine quantization as an effective method for analyzing non-renormalizable scalar fields and quantum gravity, emphasizing the importance of choosing classical variables with specific curvature properties.

Contribution

It introduces affine quantization as a promising alternative to canonical quantization for non-renormalizable models and gravity, highlighting the role of curvature in selecting classical variables.

Findings

Affine quantization effectively handles non-renormalizable scalar models.

Affine variables with negative curvature facilitate analysis of Einstein's gravity.

The approach offers new insights into quantum gravity formulations.

Abstract

Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with non-renormalizable scalar models as well as quantum gravity. The basic applications of this approach lead to the common goals of any quantization, such as Schroedinger's representation and Schroedinger's equation. Careful attention is paid toward seeking favored classical variables, which are those that should be promoted to the principal quantum operators. This effort leads toward classical variables that have a constant positive, zero, or negative curvature, which typically characterize such favored variables. This focus leans heavily toward affine variables with a constant negative curvature, which leads to a surprisingly accommodating analysis of non-renormalizable scalar models as well as Einstein's general relativity.