CPTandCPproperties of Majorana particles, and the consequences

Since a Majorana neutrino is its own antiparticle under $\mathrm{CPT}$, rather than $C$, an analysis of the $\mathrm{CPT}$ and $\mathrm{CP}$ characteristics of a Majorana particle is performed. The $\mathrm{CPT}$ transformation properties of a Majorana particle of arbitrary spin are obtained in a very simple way. Implications of these properties for the electromagnetic matrix elements of Majorana particles of spin ½ are derived. Finally, the question of when different Majorana neutrinos will make opposing contributions to neutrinoless double-$\beta$ decay is answered.