 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2015/s7/3/1/solution

The canonical Poisson bracket is

{f, g} = \sum_{k} (\frac{\partial f}{\partial q _{k}} \frac{\partial g}{\partial p _{k}} - \frac{\partial f}{\partial p _{k}} \frac{\partial g}{\partial q _{k}}) .

The coordinate derivatives are Kronecker deltas, so direct substitution gives

{q_{i}, q_{j}} = 0, {p_{i}, p_{j}} = 0, {q_{i}, p_{j}} = δ_{ij} .

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