We describe a novel class of quantum mechanical particle oscillations in both relativistic and nonrelativistic systems based on 𝒫⁢𝒯 symmetry and 𝒯2=−1 (relevant for fermions), where 𝒫 is parity and 𝒯 is time reversal. The Hamiltonians are chosen at the outset to be self-adjoint with respect to a 𝒫⁢𝒯 inner product. The quantum mechanical time evolution is based on a modified 𝒞⁢𝒫⁢𝒯 inner product constructed in terms of a suitable 𝒞 operator. The resulting quantum mechanical evolution is shown to be unitary and probability is conserved by the oscillations.

中文翻译：

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P均匀维度表示中的对称费米子粒子振荡


我们基于 PT 对称性和 T2=-1（与费米子相关）描述了相对论和非相对论系统中的一类新型量子力学粒子振荡，其中 P 是奇偶校验，T 是时间反转。哈密顿量在一开始就被选择为 PT 内积的自伴随。量子力学时间演化基于根据合适的 C 算子构建的改进的 CPT 内积。由此产生的量子力学演化被证明是幺正的，并且概率因振荡而守恒。