•Expansion of
Converted by
Mathematica
(July 10, 2003)
![test = I * NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], CDr[NM[uExpRight[x, ExpansionOrder -> do], uExpLeftAdj[x, ExpansionOrder -> do]], x, {μ}, Explicit -> True], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] /. lrRule // NMExpand // Expand // UReduce ;](../HTMLFiles/index_22.gif)
![test1 = DiscardTerms[test, Retain -> {Particle[UPerturbation] -> do}]](../HTMLFiles/index_23.gif){kind=small}
![-(2^(1/2) ∂ _ μ(Overscript[ξ^( ), ->]) · Overscript[σ, ->])/f - (öÆ^† '6 ∂ _ μ(öÆ) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2^(1/2) f) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 ∂ _ μ(öÆ))/(2^(1/2) f) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 ∂ _ μ(öÆ)^†)/(2^(1/2) f) - (öÆ '6 ∂ _ μ(öÆ)^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2^(1/2) f) - (i (öÆ^† '6 L^( ) _ μ '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 L^( ) _ μ '6 öÆ))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 R^( ) _ μ '6 öÆ^†))/(2^(1/2) f) - (i (öÆ '6 R^( ) _ μ '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)](../HTMLFiles/index_24.gif)
![ref1 = -2^(1/2)/DecayConstant[PhiMeson] CovariantNabla[xi[x], x, {μ}] /. $Substitutions /. lrRule // NMExpand // Expand // UReduce](../HTMLFiles/index_25.gif)
![-(2^(1/2) ∂ _ μ(Overscript[ξ^( ), ->]) · Overscript[σ, ->])/f - (öÆ^† '6 ∂ _ μ(öÆ) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2^(1/2) f) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 ∂ _ μ(öÆ))/(2^(1/2) f) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 ∂ _ μ(öÆ)^†)/(2^(1/2) f) - (öÆ '6 ∂ _ μ(öÆ)^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2^(1/2) f) - (i (öÆ^† '6 L^( ) _ μ '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 L^( ) _ μ '6 öÆ))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 R^( ) _ μ '6 öÆ^†))/(2^(1/2) f) - (i (öÆ '6 R^( ) _ μ '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)](../HTMLFiles/index_26.gif)
![test = I * NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], CDr[NM[uExpRight[x, ExpansionOrder -> do], uExpLeftAdj[x, ExpansionOrder -> do]], x, {μ}, Explicit -> True], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // Expand // UReduce ;](../HTMLFiles/index_30.gif)
![test2 = DiscardTerms[test, Retain -> {Particle[UPerturbation] -> do}]](../HTMLFiles/index_31.gif){kind=small}
![-(i (öÆ^† '6 ∂ _ μ(öÆ) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(4 f^2) - (i (∂ _ μ(öÆ) '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(4 f^2) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 ∂ _ μ(öÆ) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2 f^2) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(öÆ) '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2 f^2) - (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 ∂ _ μ(öÆ)))/(4 f^2) - (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(öÆ) '6 öÆ^†))/(4 f^2) + (öÆ^† '6 Overscript[L^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Overscript[L^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Overscript[L^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ)/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Overscript[R^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ^†)/(4 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Overscript[R^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (öÆ '6 Overscript[R^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)](../HTMLFiles/index_32.gif)
![SetOptions[CovariantFieldDerivative, Explicit -> True] ;](../HTMLFiles/index_33.gif){kind=small}
![ref2 = 1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], UCommutator[USmall[μ][x], xi[x]]] /. $Substitutions /. MM[x] -> NM[SMM[x], SMM[x]] // NMExpand // Expand // UReduce](../HTMLFiles/index_34.gif){kind=small}
![-(i (öÆ^† '6 ∂ _ μ(öÆ) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(4 f^2) - (i (∂ _ μ(öÆ) '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(4 f^2) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 ∂ _ μ(öÆ) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2 f^2) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(öÆ) '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2 f^2) - (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 ∂ _ μ(öÆ)))/(4 f^2) - (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(öÆ) '6 öÆ^†))/(4 f^2) + (öÆ^† '6 Overscript[L^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Overscript[L^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Overscript[L^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ)/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Overscript[R^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ^†)/(4 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Overscript[R^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (öÆ '6 Overscript[R^( ) _ μ, ->] · Overscript[σ, ->] '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)](../HTMLFiles/index_35.gif)
![SetOptions[CovariantNabla, Explicit -> False] ;](../HTMLFiles/index_38.gif){kind=small}
![Coeff[USmall][0][li_, x_] = USmall[li][x]](../HTMLFiles/index_39.gif){kind=small}
![Coeff[USmall][1][li_, x_] = -Sqrt[2]/DecayConstant[PhiMeson] CovariantNabla[xi[x], x, {li}]](../HTMLFiles/index_41.gif){kind=small}
![-(2^(1/2) ∇ _ li(Overscript[ξ^( ), ->] · Overscript[σ, ->]))/f](../HTMLFiles/index_42.gif){kind=small}
![Coeff[USmall][2][li_, x_] = 1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], UCommutator[USmall[li][x], xi[x]]]](../HTMLFiles/index_43.gif){kind=small}
![(Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 (u _ li '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] - Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 u _ li) - (u _ li '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] - Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 u _ li) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)](../HTMLFiles/index_44.gif){kind=small}
![Coeff[USmall][do_ ? ((# > 2) &)][li_, x_] := Coeff[USmall][do][li, x] = (Message[UPerturb :: nocoeff, do] ; DiscardTerms[I * NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], CDr[NM[uExpRight[x, ExpansionOrder -> do], uExpLeftAdj[x, ExpansionOrder -> do]], x, {li}, Explicit -> True], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}] // UReduce) ;](../HTMLFiles/index_46.gif)
![Coeff[USmall][3][μ, x]](../HTMLFiles/index_50.gif){kind=small}