index_2.html

•Cayley-Hamilton rules

$clr1 = CayleyHamiltonRules[{{HLeft[x], HLeft[x], NM[HRight[x], HRight[x]]}}, UDimension -> 2] /. UTrace1[(HLeft | USmall[_])[_]] -> 0$

${< H _ L '6 H _ L '6 H _ R '6 H _ R > -> 1/2 < H _ L '6 H _ L > < H _ R '6 H _ R >}$

-1/2 < Q _ L '6 Q _ L >^2 - < Q _ R '6 Q _ R > < Q _ L '6 Q _ L > - 1/2 < Q _ R '6 Q _ R >^2 + 2 < 鲃^† '6 Q _ R '6 鲃 '6 Q _ L >^2 + < Q _ L '6 Q _ L '6 Q _ L '6 Q _ L > + < Q _ R '6 Q _ R '6 Q _ R '6 Q _ R > - 2 < 鲃^† '6 Q _ R '6 鲃 '6 Q _ L '6 鲃^† '6 Q _ R '6 鲃 '6 Q _ L >

${-1/2 < Q _ L '6 Q _ L >^2, -< Q _ L '6 Q _ L > < Q _ R '6 Q _ R >, -1/2 < Q _ R '6 Q _ R >^2, 2 < 鲃^† '6 Q _ R '6 鲃 '6 Q _ L >^2, < Q _ L '6 Q _ L '6 Q _ L '6 Q _ L >, < Q _ R '6 Q _ R '6 Q _ R '6 Q _ R >, -2 < 鲃^† '6 Q _ R '6 鲃 '6 Q _ L '6 鲃^† '6 Q _ R '6 鲃 '6 Q _ L >}$

${< b '6 a '6 a > -> -1/2 < b > < a >^2 + < a '6 b > < a > + 1/2 < a '6 a > < b >}$

$su2calhamrule2 = (su2calhb[[1, 1]] /. {UMatrix[a] -> a_, UMatrix[b] -> b_}) -> (su2calhb[[1, 2]] /. {UMatrix[a] -> a, UMatrix[b] -> b})$

$su2calhamrule2 = UTrace1[NM[b___, a_, a_, c___]] :> -1/2 UTrace1[a]^2 UTrace1[NM[c, b]] + 1/2 UTrace1[NM[c, b]] UTrace1[NM[a, a]] + UTrace1[a] UTrace1[NM[a, c, b]] /; Length[{b, c}] > 0$

$< b___ '6 a_ '6 a_ '6 c___ > :> -1/2 < c '6 b > < a >^2 + < a '6 c '6 b > < a > + 1/2 < a '6 a > < c '6 b > /; Length[{b, c}] > 0$

${< a '6 a '6 a > -> 3/2 < a '6 a > < a > - < a >^3/2}$

${< a '6 a '6 a '6 a > -> -< a >^4/2 + < a '6 a > < a >^2 + 1/2 < a '6 a >^2}$

$su2qchalhamrule2 = (-1/2 * su2qchalham[[-1]] /. {μ -> μ_, x -> x_}) -> 1/2 (Plus @@ Drop[su2qchalham, {-1}]) /. su2calhamrule4$

< 鲃^† '6 Q _ R '6 鲃 '6 Q _ L '6 鲃^† '6 Q _ R '6 鲃 '6 Q _ L > -> 1/2 (-1/2 < Q _ L >^4 + < Q _ L '6 Q _ L > < Q _ L >^2 - < Q _ R >^4/2 + 2 < 鲃^† '6 Q _ R '6 鲃 '6 Q _ L >^2 + < Q _ R '6 Q _ R > < Q _ R >^2 - < Q _ L '6 Q _ L > < Q _ R '6 Q _ R >)

$clr1 = CayleyHamiltonRules[{{HLeft[x], HRight[x], NM[HLeft[x], HRight[x]]}}, UDimension -> 2] /. UTrace1[(HLeft | USmall[_])[_]] -> 0$

${< H _ L '6 H _ R '6 H _ L '6 H _ R > -> < H _ L '6 H _ R >^2 + < H _ R > < H _ R '6 H _ L '6 H _ L > - < H _ L '6 H _ L '6 H _ R '6 H _ R >}$

${2 < Q _ L '6 Q _ L > < Q _ R '6 Q _ R >, -4 < 鲃^† '6 Q _ R '6 Q _ R '6 鲃 '6 Q _ L '6 Q _ L >, 2 < 鲃^† '6 Q _ R '6 鲃 '6 Q _ L '6 Q _ L > < Q >, 2 < 鲃^† '6 Q _ R '6 Q _ R '6 鲃 '6 Q _ L > < Q >, -< Q _ L '6 Q _ L > < Q >^2, -< Q _ R '6 Q _ R > < Q >^2}$

$su2qchalhamrule3 = (-1/4 su2qchalham[[2]] /. {μ -> μ_, x -> x_}) -> 1/4 (Plus @@ Drop[su2qchalham, {2}])$

< 鲃^† '6 Q _ R '6 Q _ R '6 鲃 '6 Q _ L '6 Q _ L > -> 1/4 (-< Q _ L '6 Q _ L > < Q >^2 - < Q _ R '6 Q _ R > < Q >^2 + 2 < 鲃^† '6 Q _ R '6 鲃 '6 Q _ L '6 Q _ L > < Q > + 2 < 鲃^† '6 Q _ R '6 Q _ R '6 鲃 '6 Q _ L > < Q > + 2 < Q _ L '6 Q _ L > < Q _ R '6 Q _ R >)

$clr1 = CayleyHamiltonRules[{{HLeft[x], HLeft[x], HRight[x]}}, UDimension -> 2] /. UTrace1[(HLeft | USmall[_])[_]] -> 0$

${< H _ R '6 H _ L '6 H _ L > -> 1/2 < H _ R > < H _ L '6 H _ L >}$

${-< 鲃^† '6 Q _ R '6 鲃 '6 Q _ L '6 Q _ L >, -< 鲃^† '6 Q _ R '6 Q _ R '6 鲃 '6 Q _ L >, 1/2 < Q _ L '6 Q _ L > < Q >, 1/2 < Q _ R '6 Q _ R > < Q >, 2 < 鲃^† '6 Q _ R '6 鲃 '6 Q _ L > < Q >, -< Q >^3}$

$su2qchalhamrule4 = (-su2qchalham[[1]] /. {μ -> μ_, x -> x_}) -> (Plus @@ Drop[su2qchalham, {1}])$

Converted by Mathematica (July 10, 2003)