DiracSimplify

Description

DiracSimplify[expr] simplifies products of Dirac matrices in expr and expands non-commutative products. Double Lorentz indices and four vectors are contracted. The Dirac equation is applied. All DiracMatrix[5], DiracMatrix[6] and DiracMatrix[7] are moved to the right. The order of the other Dirac matrices is not changed.

Options[DiracSimplify]

See also:  Calc, DiracGammaExpand, DiracTrick.

Examples

This is a string of Dirac matrices in four dimensions.

t1 = GA[μ, ν, μ]

DiracSimplify[t1]

This is a string of Dirac matrices in D dimensions.

t2 = GAD[μ, ν, μ]

DiracSimplify[t1]

t3 = GA[5, μ, ν]

By default (γ^5)is moved to the right.

DiracSimplify[t3]

t4 = GA[6, μ, 7]

DiracSimplify[t4]

t5 = GS[a + b]  .  GS[p] . GS[p] . GS[c + d]

Contrary to DiracTrick DiracSimplify does non-commutative expansion.

DiracSimplify[t5]

DiracTrick[t5]

t6  =  SpinorVBar[p]  .  GS[p]  .  SpinorUBar[q]

DiracSimplify[t6]

GAD @@ Join[{μ}, Table[(Subscript[ν, i]), {i, 6}], {μ}]

DiracSimplify[%]

With the option DiracCanonical an alphabetic ordering is done.

DiracSimplify[GA[ν, μ], DiracCanonical -> True]

Setting InsideDiracTrace->True assumes that a trace is still to be taken later on.

DiracSimplify[GA[μ, ν, ρ, σ], 
      InsideDiracTrace -> True]

DiracSimplify[GA[μ, ν, ρ], 
      InsideDiracTrace -> True]

Clear[t1, t2, t3, t4, t5, t6]