Solving the commutator

$[\varphi (\vec{x}),\Pi (\vec{y})]=-i\int [d\vec{k}][d\overrightarrow{k^{\prime }}]AB(e^{i\vec{k}.\vec{x}}{e}^{-i\overrightarrow{k^{\prime }}\vec{y}}[a_k,a_{k^{\prime }}^{†}]+e^{-i\vec{k}.\vec{x}}{e}^{i\overrightarrow{k^{\prime }}\vec{y}}[a_k^{†},a_{k^{\prime }}])$

$=i\int [d\vec{k}]AB(e^{i\vec{k}(\vec{x}-\vec{y})}+\text{h.c.})=i\hslash {\delta }^3(\vec{x}-\vec{y})$

such that $\frac{2A.B}{N_k}=\hslash$ after expanding our notation.