# What's the difference between canonical quantization and second quantization?

I am wondering the difference between the canonical quantization and the second quantization in quantum field theory.

For example, a harmonic chain, one can write down its lagrangian density $$\mathcal{L}(\phi,\partial\phi/\partial t, \nabla\phi)$$, where $$\phi(\mathbf{r},t)$$ is the classical field. By replacing classical field $$\phi(\mathbf{r},t)$$ with quantum field $$\hat{\phi}(\mathbf{r},t)$$, one do the canonical quantization, which finally leads to the Hamiltonian $$$$H = \sum_k \omega_k\left( \hat{a}_k^\dagger \hat{a}_k + \frac{1}{2} \right).$$$$

However, from my understanding, the above result is obvious in second quantization where a one-particle operator can be written as the a creation-annihilation operator pair times the matrix element between these two states.

So my question is what's the difference of the two concepts?