Expanding and undoing expansions
See also
Overview.
Manipulations
FeynCalc offers further useful functions for the manipulations of Lorentz tensors and Dirac matrices. To expand scalar products
ex1 = SP[p + q + r, s + t]
(p+q+r)⋅(s+t)
or expressions like
ex2 = FV[p + q + r, \[Mu]]
(p+q+r)μ
one can use
p⋅s+p⋅t+q⋅s+q⋅t+r⋅s+r⋅t
pμ+qμ+rμ
For the expansion of Eps
tensors, we use
LC[][p1 + p2, q, r, s]
EpsEvaluate[%]
ϵˉp1+p2qrs
ϵˉp1qrs+ϵˉp2qrs
EpsEvaluate also reorders the arguments of Eps according to its antisymmetric properties
LC[\[Mu], \[Sigma], \[Rho], \[Nu]]
EpsEvaluate[%]
ϵˉμσρν
−ϵˉμνρσ
The inverse of ExpandScalarProduct
is called MomentumCombine
3 FV[p, \[Mu]] + 4 FV[q, \[Mu]]
MomentumCombine[%]
3pμ+4qμ
(3p+4q)μ
For Dirac matrices the corresponding functions are DiracGammaExpand
and DiracGammaCombine
GA[\[Mu]] . GS[p + q] . GA[\[Nu]] . GS[r + s]
DiracGammaExpand[%]
DiracGammaCombine[%]
γˉμ.(γˉ⋅(p+q)).γˉν.(γˉ⋅(r+s))
γˉμ.(γˉ⋅p+γˉ⋅q).γˉν.(γˉ⋅r+γˉ⋅s)
γˉμ.(γˉ⋅(p+q)).γˉν.(γˉ⋅(r+s))
Notice the DiracGammaExpand
does not expand the whole noncommutative product. If you need that, use DotSimplify
GA[\[Mu]] . GS[p + q] . GA[\[Nu]] . GS[r + s]
% // DiracGammaExpand // DotSimplify
γˉμ.(γˉ⋅(p+q)).γˉν.(γˉ⋅(r+s))
γˉμ.(γˉ⋅p).γˉν.(γˉ⋅r)+γˉμ.(γˉ⋅p).γˉν.(γˉ⋅s)+γˉμ.(γˉ⋅q).γˉν.(γˉ⋅r)+γˉμ.(γˉ⋅q).γˉν.(γˉ⋅s)