射影几何与$\cal PT$ -对称狄拉克哈密顿量
Projective Geometry and $\cal PT$-Symmetric Dirac Hamiltonian
摘要：
$(3 + 1)$维（广义）狄拉克方程具有相同的形式表示的条件，一个给定的点位于一个给定的线在三维射影空间中的方程。由此产生的哈密顿量与$γ_5$质量项不是厄米，但在宇称反射$\cal P$和时间反演$\cal T$的组合变换下是不变的。当$\cal PT$对称性未破缺时，自由自旋- $\frac {1}{2}$理论的能谱是实的，具有适当的位移质量。
英文摘要：
The $(3 + 1)$-dimensional (generalized) Dirac equation is shown to have the same form as the equation expressing the condition that a given point lies on a given line in 3-dimensional projective space. The resulting Hamiltonian with a $γ_5$ mass term is not Hermitian, but is invariant under the combined transformation of parity reflection $\cal P$ and time reversal $\cal T$. When the $\cal PT$ symmetry is unbroken, the energy spectrum of the free spin-$\frac {1}{2}$ theory is real, with an appropriately shifted mass.
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