A matrix element is just a number. Now, If I have the following matrix element:
\begin{equation} \newcommand\bra[1]{\left<{#1}\right|} \newcommand\ket[1]{\left|{#1}\right>} A = \bra{B}\bar{b}\gamma_{\mu}\gamma_{5}q\bar{q}\gamma^{\mu}\gamma_{5}b\ket{B} = f^{2}_{B}p_{B}^{2} \end{equation}
where b and q are quarks fields.
Is it possible to take the transpose of both sides and say that
\begin{equation} A = \bra{B}{b}^{T}\gamma_{5}^{T}(\gamma^{\mu})^{T}(\bar{q})^{T} q^{T}\gamma_{5}^{T}\gamma_{\mu}^{T}(\bar{b})^{T}\ket{B} = f^{2}_{B}p_{B}^{2} \end{equation} ?
Therefore
\begin{equation}{b}^{T}\gamma_{5}^{T}(\gamma^{\mu})^{T}(\bar{q})^{T} q^{T}\gamma_{5}^{T}\gamma_{\mu}^{T}(\bar{b})^{T}\ = \bar{b}\gamma_{\mu}\gamma_{5}q\bar{q}\gamma^{\mu}\gamma_{5}b \end{equation}
I am concerned about taking the transpose of the fermion fields because they are operators, not numbers.
