FCChargeConjugateTransposed[exp] represents the
application of the charge conjugation operator to the transposed of
exp, i.e. C^{-1} \;\text{exp}^T
C. Here exp is understood to be a single Dirac
matrix or a chain thereof. The option setting Explicit
determines whether the explicit result is returned or whether it is left
in the unevaluated form.The unevaluated form will be also maintained if
the function does not know how to obtain C^{-1} \;\text{exp}^T C from the given
exp.
The shortcut for FCChargeConjugateTransposed is
FCCCT.
Overview, SpinorChainTranspose, DiracGamma, Spinor.
GA[\[Mu], \[Nu], \[Rho]]
FCChargeConjugateTransposed[%]\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }.\bar{\gamma }^{\rho }
C\left(\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }.\bar{\gamma }^{\rho }\right)^TC^{-1}
FCChargeConjugateTransposed[GA[\[Mu], \[Nu], \[Rho]], Explicit -> True]-\bar{\gamma }^{\rho }.\bar{\gamma }^{\nu }.\bar{\gamma }^{\mu }
GA[5]
FCCCT[%]
% // Explicit\bar{\gamma }^5
C\left(\bar{\gamma }^5\right)^TC^{-1}
\bar{\gamma }^5