4DTools.nb

$RecursionLimit=Infinity

Import Adinkra package

<<Adinkra`

BuildDate[Adinkra]

Function Lists

FunctionList[SpaceTime]

FunctionList[GenerateLandR]

FunctionList[AdinkraEssentials]

FunctionList[BasisDecomposition]

FunctionList[BC4Tools]

FunctionList[GraphingTools]

FunctionList[Adinkra]

Introduction to some of these functions

Within FunctionList[SpaceTime]

η[1,1]

Cmetric

Lap[SomeField[t,x,y,z]]

Lap[A[2][t,x,y,z]]

Within FunctionList[AdinkraEssentials]

IndexRange[AdinkraEssentials][ReportLevel]

FunctionList[AdinkraEssentials]

Testing 4D space-time

γ5γ[0]

γ5.CommuteGammastdownstupdown[0,1]//MatrixForm

Cmetric//MatrixForm

UD[ψ[1][t,x,y,z],t]

Lap[ψ[1][t,x,y,z]]

Table[αmatrix[ahat]//MatrixForm,{ahat,1,3}]

γ[2].γ[3]==I αmatrix[1]

γ[3].γ[1]==I αmatrix[2]

γ[1].γ[2] == I αmatrix[3]

γ[0]==I βmatrix[3]

γ5

γ5 == -βmatrix[1]

γ[0].γ5 == βmatrix[2]

su2matrix[1,1]

αmatrix[1]

AntiCommuteGamma[2,2]

γ[5] == (-TwoTensor[1,2])

Sig[1,2] = - I (1/2)γ[1].γ[2]
Sig[2,3] = -I (1/2)γ[2].γ[3]
Sig[3,1] = -I (1/2)γ[3].γ[1]

γ[0] == I βmatrix[3]

γ[1] == αmatrix[1].βmatrix[2]

γ[2] == αmatrix[2].βmatrix[2]

γ[3] == αmatrix[3].βmatrix[2]

Sig[1,2] == (1/2)αmatrix[3]

Sig[2,3] == (1/2)αmatrix[1]

Sig[3,1] == (1/2)αmatrix[2]

γ[5] == - βmatrix[1]

-I (1/2)γ[0] == (1/2)βmatrix[3]

((-1)/2)γ[5] == (1/2)βmatrix[1]

(1/2)γ[0].γ[5] == (1/2)βmatrix[2]

βmatrix[2]//MatrixForm