•Expansion of
Converted by
Mathematica
(July 10, 2003)
![UFMinus[μ, ν][x]](../HTMLFiles/index_132.gif){kind=small}
![UFMinus[μ, ν][x] /. $Substitutions](../HTMLFiles/index_134.gif){kind=small}
![DiscardTerms[NM[uExpLeftAdj[x, ExpansionOrder -> do], FieldStrengthTensorFull[{μ}, UGeneratorMatrixIsoDotFull[QuantumField[Particle[LeftComponent[0]], {ν}][x]], x, -I], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] - NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], FieldStrengthTensorFull[{μ}, UGeneratorMatrixIsoDotFull[QuantumField[Particle[RightComponent[0]], {ν}][x]], x, -I], uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}]](../HTMLFiles/index_136.gif)
![-(i (öÆ^† '6 R^( ) _ (μ ν) '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 R^( ) _ (μ ν) '6 öÆ))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 L^( ) _ (μ ν) '6 öÆ^†))/(2^(1/2) f) - (i (öÆ '6 L^( ) _ (μ ν) '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)](../HTMLFiles/index_137.gif)
![I/Sqrt[2]/DecayConstant[Pion] UCommutator[xi[x], UFPlus[μ, ν][x]] /. $Substitutions // NMExpand // Expand](../HTMLFiles/index_138.gif){kind=small}
![-(i (öÆ^† '6 R^( ) _ (μ ν) '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 R^( ) _ (μ ν) '6 öÆ))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 L^( ) _ (μ ν) '6 öÆ^†))/(2^(1/2) f) - (i (öÆ '6 L^( ) _ (μ ν) '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)](../HTMLFiles/index_139.gif)
![DiscardTerms[NM[uExpLeftAdj[x, ExpansionOrder -> do], FieldStrengthTensorFull[{μ}, UGeneratorMatrixIsoDotFull[QuantumField[Particle[LeftComponent[0]], {ν}][x]], x, -I], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] - NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], FieldStrengthTensorFull[{μ}, UGeneratorMatrixIsoDotFull[QuantumField[Particle[RightComponent[0]], {ν}][x]], x, -I], uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}]](../HTMLFiles/index_144.gif)
![(öÆ^† '6 R^( ) _ (μ ν) '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 R^( ) _ (μ ν) '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 R^( ) _ (μ ν) '6 öÆ)/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 L^( ) _ (μ ν) '6 öÆ^†)/(4 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 L^( ) _ (μ ν) '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (öÆ '6 L^( ) _ (μ ν) '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)](../HTMLFiles/index_145.gif)
![-1/4/DecayConstant[Pion]^2 UCommutator[xi[x], UCommutator[xi[x], UFMinus[μ, ν][x]]] /. $Substitutions // NMExpand // Expand](../HTMLFiles/index_146.gif){kind=small}
![(öÆ^† '6 R^( ) _ (μ ν) '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 R^( ) _ (μ ν) '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 R^( ) _ (μ ν) '6 öÆ)/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 L^( ) _ (μ ν) '6 öÆ^†)/(4 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 L^( ) _ (μ ν) '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (öÆ '6 L^( ) _ (μ ν) '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)](../HTMLFiles/index_147.gif)
![Coeff[UFMinus][0][li1_, li2_, x_] = UFMinus[li1, li2][x]](../HTMLFiles/index_150.gif){kind=small}
![Coeff[UFMinus][1][li1_, li2_, x_] = I/Sqrt[2]/DecayConstant[Pion] UCommutator[xi[x], UFPlus[li1, li2][x]]](../HTMLFiles/index_152.gif){kind=small}
![(i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 f _ + _ (li1 li2) - f _ + _ (li1 li2) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)](../HTMLFiles/index_153.gif)
![Coeff[UFMinus][2][li1_, li2_, x_] = -1/4/DecayConstant[Pion]^2 UCommutator[xi[x], UCommutator[xi[x], UFMinus[li1, li2][x]]]](../HTMLFiles/index_154.gif){kind=small}
![-(Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 f _ - _ (li1 li2) - f _ - _ (li1 li2) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 f _ - _ (li1 li2) - f _ - _ (li1 li2) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)](../HTMLFiles/index_155.gif){kind=small}
![Coeff[UFPlus][do_ ? ((# > 2) &)][li1_, li2_, x_] := Coeff[UFMinus][do][li1, li2, x] = (Message[UPerturb :: nocoeff, do] ; DiscardTerms[NM[uExpLeftAdj[x, ExpansionOrder -> do], FieldStrengthTensorFull[{li1}, UGeneratorMatrixIsoDotFull[QuantumField[Particle[LeftComponent[0]], {li2}][x]], x, -I], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] - NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], FieldStrengthTensorFull[{li1}, UGeneratorMatrixIsoDotFull[QuantumField[Particle[RightComponent[0]], {li2}][x]], x, -I], uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}] // UReduce) ;](../HTMLFiles/index_156.gif)