P, C and T

Parity inversion $P$ is the mirror symmetry that operates by inverting the coordinates, $\bar{\bf {x}}$ $\rightarrow$ $-\bar{\bf {x}}$. Under parity inversion, the fields transform in such a way that scalars do not change sign, while pseudoscalars do. Similarly, a vector does not change sign, while axial vectors do. A Dirac spinor transforms according to $P\psi({\bf {x}},t)=\gamma_{0}\psi(-{\bf {x}},t)$.
Charge conjugation $C$ transforms a charged particle into its antiparticle. By definition the charge conjugate of the field $\phi$ is $\phi^{c}$ = $C \phi C^{-1}$. For a spin $1/2$ object $\psi$ this corresponds to $\psi^{c}$ = ${\bf {C}} \bar{\psi}^T$, where $T$ denotes the transpose and ${\bf {C}}=i\gamma^{2}\gamma^{0}$. The ${\bf {C}}$ therefore only acts on spinor indices. It satifies ${\bf {C}}^{2}=-1$, ${\bf {C}}^{\dagger}={\bf {C}}^{-1}$, ${\bf {C}}^{T}=-{\bf {C}}=-{\bf {C}}^{*}$, and ${\bf {C}}\gamma_{\mu}{\bf {C}}^{-1}=-\gamma_{\mu}^{T}$.
>From very general principles, namely Poincaré invariance, microscopic causality as expressed by local communicativity, and continuity of quantum field operators; it can be deduced that the laws of physics must be invariant under the combined operations of space reflection, time reversal and charge conjugation. This is the $CPT$ theorem, which is one of the corner stones of particle physics. Broken $CP$ thus implies broken $T$ as well.

One of the consequences of the $CPT$ invariance is the equality of masses and lifetimes of a particle and its antiparticle. Data are consistent with $CPT$ invariance. It is however not unconceivable that $CPT$ breaking could take place, namely in non-local theories, in non Lorentz invariant theories [21].