# Simplify GA[a].GA[b]+GA[b].GA[a] to 2 MT[a,b]

Does a FeynCalc command exist, that simplifies the expression

GA[a].GA[b]+GA[b].GA[a]


to

2 MT[a,b]


I've tried Calc, DiracSimplify and DiracTrick to no avail.

If not, how can I do it with vanilla Mathematica?

edit for clarification purposes.

GA[mu] refers to the GammaMatrices (https://en.wikipedia.org/wiki/Gamma_matrices). There exists an anticommutator relation that allows the anticommuter of two GammaMatrices with Minkowksi indices $$\mu$$ and $$\nu$$ to be simplified to the metric tensor element $$\eta^{\mu\nu}$$.

$$\{\gamma^\mu, \gamma^\nu\} = \gamma^\mu\gamma^\nu+\gamma^\nu\gamma^\mu = 2\eta^{\mu\nu}$$

• Why the downvote? Apr 26 '19 at 11:09
• You need to use DiracOrder or DiracSimplify with the option DiracCanonical set to True.
– vsht
Apr 26 '19 at 11:51
• You should post this as an answer as it is correct. Apr 26 '19 at 11:59