{f,g}=ω(X_f,X_g). Jacobi identity. Casimir functions. Poisson manifold.
graph TD
D1["Def: {f,g}\nω(X_f,X_g)"]
D2["Def: Jacobi\n{f,{g,h}}+cycl=0"]
D3["Def: Casimir\n{f,C}=0 ∀f"]
D4["Def: Poisson manifold\n{·,·} Lie bracket"]
T1["Thm: {f,g}=−{g,f}\nskew-sym"]
T2["Thm: Leibniz\n{f,gh}=g{f,h}+h{f,g}"]
T3["Thm: Jacobi holds\nfrom dω=0"]
T4["Thm: Symplectic⇒Poisson\nnondeg"]
T5["Thm: Dirac bracket\nconstraints"]
D1 --> T1
D2 --> T3
D1 --> T2
D3 --> T4
D4 --> T5
classDef definition fill:#b197fc,color:#fff
classDef theorem fill:#51cf66,color:#fff
class D1,D2,D3,D4 definition
class T1,T2,T3,T4,T5 theorem
Process Statistics
- Nodes: 14
- Edges: 11
Frontier: math.SG