Using Coherent States to Make Physically Correct Classical-to-Quantum Procedures that Help Resolve Nonrenomalizable Fields Including Einstein's Gravity

TL;DR

This paper advocates for affine quantization combined with coherent states to achieve physically accurate classical-to-quantum procedures, especially for nonrenormalizable fields and Einstein's gravity.

Contribution

It demonstrates that affine quantization, validated by coherent states, provides a consistent framework for quantizing nonrenormalizable fields and gravity.

Findings

Affine quantization successfully quantizes nonrenormalizable scalar fields.

Coherent states ensure physically correct quantizations.

Ultralocal models are fully soluble under affine quantization.

Abstract

Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the quantization of half-harmonic oscillators [1] nonrenormalizable scalar fields, such as $(\varphi^{12})_3$ [2], and $(\varphi^4)_4$ [3], as well as the quantum theory of Einstein's general relativity [4]. The features that distinguish affine quantization are emphasized, especially, that affine quantization differs from canonical quantization only by the choice of classical variables promoted to quantum operators. Coherent states are used to ensure proper quantizations are physically correct. While quantization of nonrenormalizable covariant scalars and gravity are difficult, we focus on appropriate ultralocal scalars and gravity which are fully soluble while, in that case, implying that affine quantization is the proper procedure to ensure the validity of affine quantizations for nonrenormalizable covariant scalar fields and Einstein's gravity.