A transformation of coordinates can be shown to be a canonical transformation if and only if it preserves these quantities, while a dynamical system is Hamiltonian if and only if the time derivative obeys the Leibniz rule on these quantities. The operator obtained by taking this quantity for the Hamiltonian and the time derivative is called the Liouvillian, which can be used to rewrite the Hamilton-Jacobi equation in terms of this quantity. The Hamiltonian Noether theorem states that this operator applied to the Hamilto
A transformation of coordinates can be shown to be a canonical transformation if and only if it preserves these quantities, while a dynamical system is Hamiltonian if and only if the time derivative obeys the Leibniz rule on these quantities. The operator obtained by taking this quantity for the Hamiltonian and the time derivative is called the Liouvillian, which can be used to rewrite the Hamilton-Jacobi equation in terms of this quantity. The Hamiltonian Noether theorem states that this operator applied to the Hamiltonian and a constant of the motion is zero. FTP, what is this concept, the classical mechanics analog of the commutator?
A transformation of coordinates can be shown to be a canonical transformation if and only if it preserves these quantities, while a dynamical system is Hamiltonian if and only if the time derivative obeys the Leibniz rule on these quantities.
Poisson Bracket or PB