In basic terms, what is relativistic canonical quantization?

Answer 1

Let's start with non-reativistic quantum mechanics. The Schrodinger equation determines how the wave function evolves as a function of time and space. But the equation has two spatial derivatives and only one time derivative. This makes it inherently non-covarient which means that it will give different answers depending on the frame of reference you do the calculation in. But Einstein showed that the laws of physics cannot depend on the frame of reference - if they did the seed of light would be different and depend on how you were moving when you measured it.

To make quantum theory consistent with relativity ( a necessity if you want to incorporate the interaction of light and matter), you need to have the same order of time derivatives as spatia derivatives. Dirac came up with an equation that does this. In the process, he had to do what is called second quantization. Essentially the wave functions from the non-relativisitic theory become a set of operators in the relativistic theory resulting in the Dirac equation.

Answer 2

"Getting something out of nothing"?