Lessons from the Light, 5.2
Note that among C, P, T, only T is an “antilinear operator” which means that
T | \lambda \psi \rangle = \lambda* T | \psi \rangle
including the asterisk which means complex conjugation (that’s the reason of the prefix, anti-). Various combinations of C, P, T are linear or antilinear depending on whether T is included.
Note that the complex conjugation is needed for the time reversal already in ordinary non-relativistic quantum mechanics because the complex conjugation is the only sensible way to change (
\exp(+ipx/\hbar) ) to (
\exp(-ipx/\hbar) ), i.e. to change the sign of the momentum p – and the velocity v = dx/dt – which is needed for particles to evolve backwards.
— BaBar directly measures time reversal violation
— Lubos Motl
2014.06.11 Wednesday ACHK