•Expansion of
Converted by
Mathematica
(July 10, 2003)
![DiscardTerms[NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], UMatrix[UChi[]][x], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] + NM[uExpLeftAdj[x, ExpansionOrder -> do], Adjoint[UMatrix[UChi[]][x]], uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}]](../HTMLFiles/index_51.gif)
![-(i (öÆ^† '6 χ '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f) - (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 χ '6 öÆ^†))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 χ^† '6 öÆ))/(2^(1/2) f) + (i (öÆ '6 χ^† '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)](../HTMLFiles/index_52.gif)
![-I/Sqrt[2]/DecayConstant[Pion] UAntiCommutator[xi[x], UChiMinus[x]] /. $Substitutions // NMExpand // Expand](../HTMLFiles/index_53.gif){kind=small}
![-(i (öÆ^† '6 χ '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f) - (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 χ '6 öÆ^†))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 χ^† '6 öÆ))/(2^(1/2) f) + (i (öÆ '6 χ^† '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)](../HTMLFiles/index_54.gif)
![DiscardTerms[NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], UMatrix[UChi[]][x], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] + NM[uExpLeftAdj[x, ExpansionOrder -> do], Adjoint[UMatrix[UChi[]][x]], uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}]](../HTMLFiles/index_59.gif)
![-(öÆ^† '6 χ '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 χ '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 χ '6 öÆ^†)/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 χ^† '6 öÆ)/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 χ^† '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (öÆ '6 χ^† '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)](../HTMLFiles/index_60.gif)
![-1/4/DecayConstant[Pion]^2 UAntiCommutator[xi[x], UAntiCommutator[xi[x], UChiPlus[x]]] /. $Substitutions // NMExpand // Expand](../HTMLFiles/index_61.gif){kind=small}
![-(öÆ^† '6 χ '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 χ '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 χ '6 öÆ^†)/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 χ^† '6 öÆ)/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 χ^† '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (öÆ '6 χ^† '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)](../HTMLFiles/index_62.gif)
![Coeff[UChiPlus][0][x_] = UChiPlus[x]](../HTMLFiles/index_65.gif){kind=small}
![Coeff[UChiPlus][1][x_] = -I/Sqrt[2]/DecayConstant[Pion] UAntiCommutator[xi[x], UChiMinus[x]]](../HTMLFiles/index_67.gif){kind=small}
![-(i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 χ _ - + χ _ - '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)](../HTMLFiles/index_68.gif)
![Coeff[UChiPlus][2][x_] = -1/4/DecayConstant[Pion]^2 UAntiCommutator[xi[x], UAntiCommutator[xi[x], UChiPlus[x]]]](../HTMLFiles/index_69.gif){kind=small}
![-(Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 χ _ + + χ _ + '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 χ _ + + χ _ + '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)](../HTMLFiles/index_70.gif){kind=small}
![Coeff[UChiPlus][2][x] // UTrace // NMExpand // CycleUTraces](../HTMLFiles/index_71.gif){kind=small}
![-< χ _ + '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] >/f^2](../HTMLFiles/index_72.gif)
![Coeff[UChiPlus][do_ ? ((# > 2) &)][x_] := Coeff[UChiPlus][do][x] = (Message[UPerturb :: nocoeff, do] ; DiscardTerms[NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], UMatrix[UChi[]][x], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] + NM[uExpLeftAdj[x, ExpansionOrder -> do], Adjoint[UMatrix[UChi[]][x]], uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}] // UReduce) ;](../HTMLFiles/index_73.gif)