CPTTransformation

CPTTransformation refers to the combined symmetry operation formed by charge conjugation (C), parity transformation (P), and time reversal (T) acting on quantum fields and states. The CPT operator is the composition of these three operations and, in most formulations, is antiunitary due to the time-reversal component. Under CPT, particles are mapped to their antiparticles, spatial coordinates are inverted, and the direction of time is reversed, with corresponding transformations applied to the fields and their amplitudes.

In field-theoretic terms, CPT acts on a field by transforming its internal quantum numbers, reversing momenta and helicities as appropriate, and producing a state that corresponds to the antiparticle with inverted charges. For Dirac fields, this involves a specific rearrangement of spinor components together with charge conjugation and complex conjugation. The exact representation depends on the field content, but the general consequence is that a CPT transformation relates a process to its CPT-conjugate process.

The CPT theorem states that any local, Lorentz-invariant quantum field theory with a Hermitian Hamiltonian has CPT symmetry. As a result, the S-matrix remains invariant under CPT, implying identical properties for particles and their antiparticles, such as masses and total decay widths. It also enforces constraints on magnetic moments and other intrinsic quantities, up to sign conventions dictated by the transformations.

Experimentally, CPT invariance is strongly supported. No CPT violation has been observed, with stringent limits arising from precision measurements in neutral meson systems, baryons, leptons, and their magnetic moments. Observing CPT violation would indicate foundational breaks in locality, Lorentz invariance, or unitarity, prompting revisions to current theoretical frameworks.

In theoretical research, CPT invariance is a cornerstone, while explorations of possible CPT violation often employ frameworks like the Standard-Model Extension to parameterize and search for tiny violations across multiple sectors.