symplectic geometry. phase space with 2-form ω, Hamiltonian flows, canonical transformations, conservation laws
| Op | Action |
|---|---|
symplectic_form(M) |
Define closed non-degenerate 2-form ω |
hamiltonian(H, q, p) |
Specify Hamiltonian function |
flow(H, state, dt) |
Symplectic integration step |
poisson(f, g) |
Poisson bracket {f, g} |
canonical(T) |
Verify canonical transformation |
conserved(H, f) |
Test if f is conserved under H |
action(L, path) |
Compute action integral |
natural language of classical and semi-classical mechanics. required for: physical simulation with energy conservation, quantum-classical interface, molecular dynamics. the conservation law structure (ω is closed: dω = 0) has no analog in Clifford or Riemannian geometry. research horizon
see cyb/languages for the complete language set. see cyb/multiproof for the proving architecture