Beginning with Eq. (14.50), prove Eq. (14.52), and derive the chiral decompositions given for \(\bar{\psi} \psi, \bar{\psi} \gamma^{\mu} \psi\), and \(\bar{\psi} \gamma^{\mu} \gamma^{5} \psi\) interactions in Eqs. (14.53) and (14.54).

Data from Eq. 14.50

Data from Eq. 14.52

Data from Eq. 14.53

Data from Eq. 14.54

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= R+LUR + ULP++ P.