Question

What is poission bracket condotion to be transformation is canonical.

Answer 1

Answer

Transformation is canonical if the fundamental poisson bracket is preserved

Can be written as

$\{\tilde{p_i}\space \tilde{p_j} \}=0 \quad \{\tilde{q_i}\space \tilde{q_j} \}=0\\\{\tilde{q_i}\space \tilde{p_j} \}=\delta_{ij}$