Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 301 / 2 / iv / Solution

The canonical quantization of a real scalar field promotes the classical equal-time brackets to the canonical commutation relations, in units $\hslash =1$:The Dirac delta distribution expresses locality of the conjugate variables. These are identities of operator-valued distributions, interpreted after spatial smearing where necessary.