on which Hamiltonian mechanics plays out.

The tautological one-form

The cotangent bundle carries a canonical one-form also known as the symplectic potential, Poincaré 1-form, or Liouville 1-form. This means that if we regard as a manifold in its own right, there is a canonical section of the vector bundle over .

This section can be constructed in several ways. The most

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