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- W3088094413 abstract "We study faithful representations of the discrete Lorentz symmetry operations of parity $mathbf P$ and time reversal $mathbf T$, which involve complex phases when acting on fermions. If the phase of $mathbf P$ is a rational multiple of $pi$ then $mathbf P^{2 n}=1$ for some positive integer $n$ and it is shown that, when this is the case, $mathbf P$ and $mathbf T$ generate a discrete group, a dicyclic group (also known as a generalised quaternion group) which are generalisations of the dihedral groups familiar from crystallography. Charge conjugation $mathbf C$ introduces another complex phase and, again assuming rational multiples of $pi$ for complex phases, $mathbf T mathbf C$ generates a cyclic group of order $2 m$ for some positive integer $m$.There is thus a doubly infinite series of possible finite groups labelled by $n$ and $m$. Demanding that $mathbf C$ commutes with $mathbf P$ and $mathbf T$ forces $n=m=2$ and the group generated by $mathbf P$ and $mathbf T$ is uniquely determined to be the quaternion group. Neutral pseudo-scalar mesons can be simultaneous $mathbf C$ and $mathbf P$ eigenstates. $mathbf T$ commutes with $mathbf P$ and $mathbf C$ when acting on fermion bi-linears so neutral pseudo-scalar mesons can also be $mathbf T$ eigenstates. The $mathbf T$-parity should therefore be experimentally observable and the $mathbf{CPT}$ theorem dictates that $T= C P$." @default.
- W3088094413 created "2020-10-01" @default.
- W3088094413 creator A5031946190 @default.
- W3088094413 date "2020-09-26" @default.
- W3088094413 modified "2023-09-27" @default.
- W3088094413 title "On the group generated by $mathbf C$, $mathbf{P}$ and $mathbf T$: $mathbf {I^2 = T^2 = P^2 = I T P= -1}$, with applications to pseudo-scalar mesons" @default.
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