The 1-form λ = p dq − H dt on extended phase space has a closed 2-form dλ = ω − dH ∧ dt which is preserved along the Hamiltonian flow. Consequently the integral of p dq − H dt around any loop transported by the flow is invariant in time —…
The 1-form λ = p dq − H dt on extended phase space has a closed 2-form dλ = ω − dH ∧ dt which is preserved along the Hamiltonian flow. Consequently the integral of p dq − H dt around any loop transported by the flow is invariant in time —…