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theorems:cpt

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CPT Theorem

Intuitive

Explanations in this section should contain no formulas, but instead, colloquial things like you would hear them during a coffee break or at a cocktail party.

Concrete

The CPT theorem says that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must be CPT symmetric.

Abstract

  • The standard reference is "PCT, spin and statistics, and all that" by R. F. Streater and A. S. Wightman.
  • For a nice discussion of the symmetry groups involved see The Pin Groups in Physics: C, P, and T by M. Berg, C. DeWitt-Morette, S. Gwo, E. Kramer

Why is it interesting?

The CPT theorem tells us that CPT symmetry holds for all physical phenomena.

Research

FAQ

Why, exactly, is the CPT theorem considered so holy?

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

theorems/cpt.1522063363.txt.gz · Last modified: 2018/03/26 11:22 (external edit)