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arXiv · 1609.02255

The geometry properties of parity and time reversal operators in two dimensional spaces

Minyi Huang·Yu Yang·Junde Wu·Minhyung Cho
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Abstract

The parity operator $\cal P$ and time reversal operator $\cal T$ are two important operators in the quantum theory, in particular, in the $\cal PT$-symmetric quantum theory. By using the concrete forms of $\cal P$ and $\cal T$, we discuss their geometrical properties in two dimensional spaces. It is showed that if $\cal T$ is given, then all $\cal P$ links with the quadric surfaces; if $\cal P$ is given, then all $\cal T$ links with the quadric curves. Moreover, we give out the generalized unbroken $\cal PT$-symmetric condition of an operator. The unbroken $\cal PT$-symmetry of a Hermitian operator is also showed in this way.

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Minyi Huang, Yu Yang, Junde Wu, Minhyung Cho. 2016-09-08. The geometry properties of parity and time reversal operators in two dimensional spaces. https://arxiv.org/abs/1609.02255

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