  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.
