Quantisation

To quantise our theory, we need to input the uncertainty principle. Again, parallels help:

$[X,P]=i\hslash ⟹[\varphi ,\Pi ]=i\hslash 1$.

Just like we cannot measure momentum and position simultaneously and to arbitrary precision, we cannot determine the field value and its time derivative to arbitrary precision either. So, we promote $\varphi ,\Pi$ to operators and impose a form that satisfies commutation relations.

• The Quantum Harmonic Oscillator
• Fock Space and Operators
• Connection with “old” QM
• Causality