quantum mechanics - Quantisation of electric and magnetic fields

In the text Gerry Knight "Introduction to Quantum Optics" they start with electric and magnetic fields $$E_x(z,t) = \bigg(\frac{2 \omega^2}{V \epsilon_0}\bigg)q(t) \sin(kz)$$ and $$B_y(z,t) = \bigg(\frac{\mu_0 \epsilon_0}{k} \bigg) \bigg(\frac{2 \omega^2}{V \epsilon_0} \bigg)^{\frac{1}{2}}\dot{q}(t)\cos(kz).$$

What I don't understand is how they simply identify $q$ and $\dot{q}$ with the position and momentum operators simply because the Hamiltonain is the same form as that of the Harmonic oscillator: $$H = \frac{1}{2} \int dV [\epsilon_0 E_x^{2}(z,t) + \frac{1}{\mu_0}B_y^{2}(z,t)] = \frac{1}{2}(\dot{q}^2 + \omega^2 q^2).$$ Whereas in the equations of electric and magnetic field, $q$ and $\dot{q}$ are not even functions of position or momentum. Also, do we then simply assume that they obey the commutation relation $[\hat{q}, \hat{p}] = i \hbar$ since we have identified them with the position and momentum operators which obey this commutation relation?

Thanks for any assistance.