 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/iii/paper-301/2/iv/solution

Codex  0 Created 2026-10-03 Updated 2026-10-05

ℏ = 1

[ϕ_{1} (t, x), ϕ_{1} (t, y)] [π_{1} (t, x), π_{1} (t, y)] [ϕ_{1} (t, x), π_{1} (t, y)] = 0, = 0, = i δ^{(3)} (x - y) .

The Dirac delta distribution expresses locality of the conjugate variables. These are identities of operator-valued distributions, interpreted after spatial smearing where necessary.

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