40 questions linked to/from Which transformations are canonical?
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### Condition for a time-dependent transformation to be a canonical transformation [duplicate]

I'm looking for a sufficient condition to determine if a given transformation is a canonical transformation. I have found two conditions, but they are only valid for the case that the transformation ...
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### Momentum vector transformation

I am confused about the way momentum vector transforms in the following case: $$q_k \to q_k'= q_k + \epsilon f_k(q)$$ The Jacobian is thus \$\Lambda_{ij} = \frac{\partial q'_i}{\partial q_j} \approx \...
I have a volume element in phase space: $$d\omega = \prod _{i=1}^{N}(dq_{i},dp_{i})$$ Now I should show the invariance of this product under canonical transformations. I think first I would have to ...