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

  • Min-yi Huang
  • Yu Yang
  • Jun-de Wu
  • Min-Hyung ChoEmail author


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


PT-symmetry geometrical property unbroken condition 

MR Subject Classification



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Copyright information

© Editorial Committee of Applied Mathematics 2019

Authors and Affiliations

  • Min-yi Huang
    • 1
  • Yu Yang
    • 2
  • Jun-de Wu
    • 1
  • Min-Hyung Cho
    • 3
    Email author
  1. 1.School of Mathematical ScienceZhejiang UniversityHangzhouPeople’s Republic of China
  2. 2.Department of MathematicsNational University of SingaporeSingaporeRepublic of Singapore
  3. 3.Department of Applied MathematicsKumoh National Institute of TechnologyKyungbukKorea

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