•Expansion of K _ a^b

do = 1

1

KW[b, a][x]

K _ a^b

KW[b, a][x] /. $Substitutions

öÆ '6 Q _ a^b '6 öÆ^†

DiscardTerms[NM[uExpLeftAdj[x, ExpansionOrder -> do], QW[b, a], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] /. lrRule // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}]

(i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ a^b '6 öÆ^†))/(2^(1/2) f) - (i (öÆ '6 Q _ a^b '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)

I/Sqrt[2]/DecayConstant[PhiMeson] UCommutator[xi[x], KW[b, a][x]] /. $Substitutions /. lrRule // NMExpand // Expand

(i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ a^b '6 öÆ^†))/(2^(1/2) f) - (i (öÆ '6 Q _ a^b '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)

% - %%

0

do = 2

2

DiscardTerms[NM[uExpLeftAdj[x, ExpansionOrder -> do], QW[b, a], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] /. lrRule // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}]

-(Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ a^b '6 öÆ^†)/(4 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ a^b '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (öÆ '6 Q _ a^b '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)

-1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], UCommutator[xi[x], KW[b, a][x]]] /. $Substitutions /. lrRule // NMExpand // Expand

-(Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ a^b '6 öÆ^†)/(4 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ a^b '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (öÆ '6 Q _ a^b '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)

% - %%

0

Coeff[KW][0][a_, b_, x_] = KW[a, b][x]

f _ + _ (li1 li2)

Coeff[KW][1][a_, b_, x_] = I/Sqrt[2]/DecayConstant[PhiMeson] UCommutator[xi[x], KW[a, b][x]]

(i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 K _ b^a - K _ b^a '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)

Coeff[KW][2][a_, b_, x_] = -1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], UCommutator[xi[x], KW[a, b][x]]]

-(Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 K _ b^a - K _ b^a '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 K _ b^a - K _ b^a '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)

Coeff[KW][do_ ? ((# > 2) &)][a_, b_, x_] := Coeff[KW][do][a, b, x] = (Message[UPerturb :: nocoeff, do] ; DiscardTerms[NM[uExpLeftAdj[x, ExpansionOrder -> do], QW[a, b], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}] // UReduce) ;

Coeff[KW][4][a, b, x]

UPerturb :: nocoeff : Warning: Yor are requesting expanding in UPerturbation to order 4 . Only up to order 2 is implemented in terms of USmall and CovariantNabla.  (If you have the energy, please do work out the expansion and send it to feyncalc@feyncalc.org).

(Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ b^a '6 öÆ^†)/(96 f^4) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ b^a '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(24 f^4) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ b^a '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(16 f^4) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ b^a '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(24 f^4) + (öÆ '6 Q _ b^a '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(96 f^4)

Converted by Mathematica  (July 10, 2003)