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The CPT theorem says that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must be CPT symmetric.
The CPT theorem tells us that CPT symmetry holds for all physical phenomena.
Because the CPT theorem is an almost-consequence of Lorentz invariance.
If you have a Lorentz invariant theory, then you can change the coordinates of space time with the following matrix and leave the theory the same
cosh(y) 0 0 sinh(y) 0 1 0 0 0 0 1 0 sinh(y) 0 0 cosh(y) and this is true for any y.
An interesting property of quantum mechanics is that the amplitudes you calculate are analytic functions of the variables in the problem, this is an obvious fact in perturbation theory, where the amplitudes are just rational functions of the momenta coming in and going out, but its more general than that. The amplitudes are analytic in a wide range of circumstances.
And this means that the theory is invariant for any complex value of y, by the principle of analytic continuation. In particular, for y=−1=i and if you stick in y=i, you get that the matrix above does a PT transformation. So that a theory of a bunch of scalar particles is PT invariant.
A more general result, if you allow charged particles, is that a general theory is CPT invariant; the argument is essentially the same.Ron Maimon