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【SEOtext】0.General Formulation,a.Velocity,Velocity is defined as a function Vc∈C(C2) by the equation:Vc(z(x1,x2),z(y1,y2))=z(V1(x,y),V2(x,y)),x,y∈R2.Then it follows that:∀ξ,η∈C;{η=∂Lc(ξ,ξ†;Vc(ξ,η),Vc†(ξ,η))/∂Vc†(ξ,η),η†=∂Lc(ξ,ξ†;Vc(ξ,η),Vc†(ξ,η))/∂Vc(ξ,η)These conditions determine Vc completely.b.Hamiltonian,Hamiltonian is defined as a function Hc∈C(C4) such that:∀x,y∈R2;Hc(z(x1,x2),z†(x1,x2);z(y1,y2),z†(y1,y2))=H(x,y)Then it follows that:∀ξ,η∈C;Hc(ξ,ξ†;η,η†)=η†Vc(ξ,η)+ηVc†(ξ,η)-Lc(ξ,ξ†;Vc(ξ,η),Vc†(ξ,η)),c.Canonical Equations,If u(t)=z(q1(t),q2(t)) and v(t)=z(p1(t),p2(t)) then the canonical equations (iii) are equivalent to the following equations.{∂Hc(u(t),u†(t);v(t),v†(t))/∂v(t)=∂0u†(t),∂Hc(u(t),u†(t);v(t),v†(t))/∂v†(t)=∂0u(t),∂Hc(u(t),u†(t);v(t),v†(t))/∂u(t)=-∂0v†(t)