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A state space carrying positions and conjugate momenta, ordinarily a symplectic manifold in Hamiltonian mechanics.
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For a smooth configuration manifold , the standard phase space is the new manifold with its canonical symplectic form; it is not the same carrier with extra data.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
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Hamiltonian phase spaces are symplectic manifolds or appropriate generalizations.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
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Classical statistical mechanics represents each microscopic state as a phase-space point and ensembles as measures or densities over phase space, subject to the selected Hamiltonian and constraints.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
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A symplectic or Poisson phase space supplies a Poisson bracket on observables.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
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