The Benefits of Affine Quantization

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.