Constraints imposed by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>conservation in the presence of pseudoparticles

We elaborate on an earlier discussion of $\mathrm{CP}$ conservation of strong interactions which includes the effect of pseudoparticles. We discuss what happens in theories of the quantum-chromodynamics type when we include weak and electromagnetic interactions. We find that strong $\mathrm{CP}$ conservation remains a natural symmetry if the full Lagrangian possesses a chiral U(1) invariance. We illustrate our results by considering in detail a recent model of (weak) $\mathrm{CP}$ nonconservation.