Knecht and Urech's result for
n
=2:
Converted by
Mathematica
(July 10, 2003)
![knechtsu2res = 1/12 * UTrace[NM[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]]] * UTrace[NM[CovariantFieldDerivative[MM[x], x, LorentzIndex[ν]], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[ν]]]]] + 1/6 * UTrace[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[ν]]]]^2 - 1/32 * (UTrace[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]] + UTrace[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]])^2 + 1/2 * (UTrace[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ1]]], CovariantFieldDerivative[UMatrix[UChi[]][x], x, LorentzIndex[μ1]]]] + UTrace[NM[Adjoint[CovariantFieldDerivative[UMatrix[UChi[]][x], x, LorentzIndex[μ1]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ1]]]]) - 1/6 * UTrace[NM[GRight[LorentzIndex[μ], LorentzIndex[ν]][x], MM[x], GLeft[LorentzIndex[μ], LorentzIndex[ν]][x], Adjoint[MM[x]]]] - I/6 * (UTrace[NM[GLeft[LorentzIndex[μ], LorentzIndex[ν]][x], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[ν]]] + NM[GRight[LorentzIndex[μ], LorentzIndex[ν]][x], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[ν]]]]]) + 1/2 * UTrace[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChi[]][x]]] - 1/12 * (UTrace[NM[GLeft[LorentzIndex[μ], LorentzIndex[ν]][x], GLeft[LorentzIndex[μ], LorentzIndex[ν]][x]]] + UTrace[NM[GRight[LorentzIndex[μ], LorentzIndex[ν]][x], GRight[LorentzIndex[μ], LorentzIndex[ν]][x]]]) + 1/2 * ( Det[Adjoint[UMatrix[UChi[]][x]]] + Det[UMatrix[UChi[]][x]]) + 1/6 * FieldStrengthTensor[LorentzIndex[μ], QuantumField[Vector[1], LorentzIndex[ν]][x], x, Explicit -> False]^2 * UTrace[UMatrix[UChiralSpurion[]][x]]^2 - 3 * f^2/4 * UTrace[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]] * (UTrace[NM[UMatrix[UChiralSpurionRight[]][x], UMatrix[UChiralSpurionRight[]][x]]] + UTrace[NM[UMatrix[UChiralSpurionLeft[]][x], UMatrix[UChiralSpurionLeft[]][x]]]) + (3/4 - z) f^2 * UTrace[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]] * UTrace[UMatrix[UChiralSpurion[]][x]]^2 + 2 * z * f^2 * UTrace[NM[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]], Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]]]] * UTrace[NM[UMatrix[UChiralSpurionRight[]][x], MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]]]] - 3 * f^2/4 * (UTrace[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], UMatrix[UChiralSpurionRight[]][x], MM[x]]] * UTrace[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], UMatrix[UChiralSpurionRight[]][x], MM[x]]] + UTrace[NM[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]]]] * UTrace[NM[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]]]]) + 2 * z * f^2 * UTrace[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], UMatrix[UChiralSpurionRight[]][x], MM[x]]] * UTrace[NM[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]]]] - f^2/8 * (UTrace[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]] + UTrace[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]) * (UTrace[NM[UMatrix[UChiralSpurionRight[]][x], UMatrix[UChiralSpurionRight[]][x]]] + UTrace[NM[UMatrix[UChiralSpurionLeft[]][x], UMatrix[UChiralSpurionLeft[]][x]]]) - z * f^2 * (UTrace[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]] + UTrace[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]) * UTrace[NM[UMatrix[UChiralSpurion[]][x]]]^2 + (1/4 + 2 * z) f^2 * (UTrace[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]] + UTrace[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]) * UTrace[NM[UMatrix[UChiralSpurionRight[]][x], MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]]]] + (1/8 - z) * f^2 * UTrace[NM[NM[UMatrix[UChi[]][x], Adjoint[MM[x]]] - NM[MM[x], Adjoint[UMatrix[UChi[]][x]]], UMatrix[UChiralSpurionRight[]][x], MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]]] + NM[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]] - NM[Adjoint[MM[x]], UMatrix[UChi[]][x]], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], MM[x]]] + f^2/4 * UTrace[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], UCommutator[CQRight[LorentzIndex[μ]][x], UMatrix[UChiralSpurionRight[]][x]], MM[x]] + NM[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]], UCommutator[CQLeft[LorentzIndex[μ]][x], UMatrix[UChiralSpurionLeft[]][x]], Adjoint[MM[x]]]] + f^2/4 * UTrace[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]]], UMatrix[UChiralSpurionRight[]][x], MM[x], CQLeft[LorentzIndex[μ]][x]] + NM[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ]], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]], CQRight[LorentzIndex[μ]][x]]] + (3/2 + 3 * z + 12 * z^2) * f^4 * UTrace[NM[UMatrix[UChiralSpurionRight[]][x], MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]]]]^2 - 3 * f^4/2 * UTrace[NM[UMatrix[UChiralSpurionRight[]][x], MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]]]] * UTrace[NM[UMatrix[UChiralSpurionRight[]][x], UMatrix[UChiralSpurionRight[]][x]] + NM[UMatrix[UChiralSpurionLeft[]][x], UMatrix[UChiralSpurionLeft[]][x]]] - (3 * z + 12 * z^2) * f^4 * UTrace[NM[UMatrix[UChiralSpurionRight[]][x], MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]]]] * UTrace[UMatrix[UChiralSpurion[]][x]]^2 + (3/8 - 3/4 * z + z^2) * f^4 * UTrace[NM[UMatrix[UChiralSpurionRight[]][x], UMatrix[UChiralSpurionRight[]][x]] + NM[UMatrix[UChiralSpurionLeft[]][x], UMatrix[UChiralSpurionLeft[]][x]]]^2 + (3 * z/2 - 2 * z^2) * f^4 * UTrace[NM[UMatrix[UChiralSpurionRight[]][x], UMatrix[UChiralSpurionRight[]][x]] + NM[UMatrix[UChiralSpurionLeft[]][x], UMatrix[UChiralSpurionLeft[]][x]]] * UTrace[UMatrix[UChiralSpurion[]][x]]^2 - z^2 * f^4 * UTrace[NM[UMatrix[UChiralSpurionRight[]][x], UMatrix[UChiralSpurionRight[]][x]] - NM[UMatrix[UChiralSpurionLeft[]][x], UMatrix[UChiralSpurionLeft[]][x]]]^2 + 4 * z^2 * f^4 * UTrace[UMatrix[UChiralSpurion[]][x]]^4](../HTMLFiles/index_422.gif)
