The Benefits of Affine Quantization

TL;DR

Affine quantization offers a novel approach that overcomes limitations of canonical quantization, enabling the quantization of complex systems like scalar fields with quartic interactions and Einstein's gravity.

Contribution

This paper introduces affine quantization as a new method that successfully addresses problems where canonical quantization fails, expanding the scope of quantizable classical systems.

Findings

Affine quantization solves quartic scalar field theories in higher dimensions.

It enables the quantization of Einstein's gravity in four spacetime dimensions.

Affine quantization overcomes limitations of canonical methods in complex systems.

Abstract

Canonical quantization has served wonderfully for the quantization of a vast number of classical systems. That includes single classical variables, such as $p$ and $q$, and numerous classical Hamiltonians $H(p,q)$, as well as field theories, such as $\pi(x)$ and $ \phi(x)$, and many classical Hamiltonians $H(\pi,\phi)$. However, in all such systems there are situations for which canonical quantization fails. This includes certain particle and field theory problems. Affine quantization involves a simple recombination of classical variables that lead to a new chapter in the process of quantization, and which is able to solve a vast variety of normally insoluble systems, such as quartic interactions in scalar field theory in spacetime dimensions 4 and higher, as well as the quantization of Einstein's gravity in 4 spacetime dimensions.