# CPT symmetry

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CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.

## Contents

### History

Efforts during the late 1950s revealed the violation of P-symmetry by phenomena that involve the weak force, and there were well-known violations of C-symmetry as well. For a short time, the CP-symmetry was believed to be preserved by all physical phenomena, but that was later found to be false too, which implied, by CPT invariance, violations of T-symmetry as well. The CPT theorem requires the preservation of CPT symmetry by all physical phenomena. It assumes the correctness of quantum laws and Lorentz invariance. Specifically, the CPT theorem states that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.

The CPT theorem appeared for the first time, implicitly, in the work of Julian Schwinger in 1951 to prove the connection between spin and statistics. In 1954, Gerhart Lüders and Wolfgang Pauli derived more-explicit proofs, so this theorem is sometimes known as the Lüders-Pauli theorem. At about the same time, and independently, this theorem was also proved by John Stewart Bell. These proofs are based on the validity of Lorentz invariance and the Principle of locality in the interaction of quantum fields. Subsequently Res Jost gave a more general proof in the framework of axiomatic quantum field theory.

### Derivation

Consider a Lorentz boost in a fixed direction z. This can be interpreted as a rotation of the time axis into the z axis, with an imaginary rotation parameter. If this rotation parameter were real, it would be possible for a 180° rotation to reverse the direction of time and of z. Reversing the direction of one axis is a reflection of space in any number of dimensions. If space has 3 dimensions, it is equivalent to reflecting all the coordinates, because an additional rotation of 180° in the x-y plane could be included.

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