Canonical quantization of a real scalar field
= Canonical quantization of a real scalar field
The equal-time <canonical commutation relation> is $[\phi(t,\mathbf x),\pi(t,\mathbf y)]=i\delta^3(\mathbf x-\mathbf y)$ in units $\hbar=1$, with the two field-field and momentum-momentum commutators zero. The quadratic <Hamiltonian operator> gives $\dot\phi=\pi$ and $\dot\pi=\nabla^2\phi-m^2\phi$, hence the <Klein-Gordon equation> as an operator identity.