Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 47 / 4 / a / Solution

Define ${\Pi }^{\mu }{}_{\nu }=\mathrm{diag}(1,-1,-1,-1)$ and $x_P=(x^0,-\mathbf{x})$. In a conventional intrinsic-phase choice, the charged W boson transforms under CP symmetry asThus its time component maps to minus the conjugate time component, and its spatial components map to plus the conjugate spatial components. Charge is exchanged, the Lorentz index undergoes parity, and the overall minus sign is a consistent phase convention shared with the charged-current transformation. The analogous formula exchanges $W^{-}$ with $W^{+}$.