SetDirectory["C:\\drorbn\\AcademicPensieve\\2012-01"];
<< betaCalculus.m

{ar[1,1] ** R[1,2], R[1,2]**ar[1,1]}

(V=W[ω]+ α ar[1,1] + β ar[1,2] + γ ar[2,1] + δ ar[2,2]) // βForm

Vα = α ar[1,1]

{Vα**dΔ[1,1,2][R[1,3]], R[1,3]**R[2,3]**Vα, Vα**R[1,3]**R[2,3]} // βForm

{t1=V**dΔ[1,1,2][R[1,3]], t2=R[1,3]**R[2,3]**V} // βForm

{t1, t2} /. {β|γ|δ -> 0, _W -> 0} // βForm