论文标题
在$ \ mathbf c $，$ \ mathbf {p} $和$ \ mathbf t $中生成的组上
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
论文作者
论文摘要
我们研究了平均$ \ mathbf p $和时间逆转$ \ mathbf t $的离散Lorentz对称操作的忠实表示，该操作涉及在费米子上行动时复杂的阶段。 If the phase of $\mathbf P$ is a rational multiple of $π$ 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晶体学。电荷共轭$ \ MATHBF C $引入了另一个复杂阶段，并且再次假设复杂阶段的$π$的合理倍数，$ \ Mathbf t \ Mathbf C $生成了一个周期性的订单$ 2 m $的$ 2 m $的$ M $。因此，有一个$ n $ $ n $ $ n $ $ n $ $ n $ $ n $ m $ $ m $。要求使用$ \ mathbf p $和$ \ mathbf t $ n = m = 2 $的$ \ mathbf c $通勤，而由$ \ mathbf p $和$ \ mathbf t $产生的组被独特地确定为quaternion组。 中性伪量表介子可以同时发生$ \ mathbf c $和$ \ mathbf p $ eigenstates。 $ \ mathbf t $通勤使用$ \ mathbf p $和$ \ mathbf c $在Fermion Bi-linears作用时，中性的伪量表中也可以是$ \ mathbf t $ eigenstates。因此，应在实验上可观察到$ \ Mathbf T $ - Parity，并且$ \ Mathbf {cpt} $定理指示$ t = c p $。
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 $π$ 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 $π$ 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 $T= C P$.
