# CP-symmetry and Ward identities and finite temperature

I have a few questions about Ward-identities which I summarize here. For each I am very greateful for answers and references to literature.

1. Taken seriously this means that Ward-Takahashi identities also exist for discrete symmetries like CP (if present in the Lagrangian) in contrast to a conserved Noether current. If so, I wonder if CP relations between amplitudes, such as $|\mathcal{M}|_{S_i\rightarrow S_f} =|\mathcal{M}|_{\bar{S}_i\rightarrow \bar{S}_f}$ which I can get by computing the amplitudes in perturbation theory and comparing, can be considered Ward-identities. $\bar{S}_{i,f}$ are the CP-conjugated states of ${S}_{i,f}$ respectively.