PT symmetry in relativistic quantum mechanics

Abstract

In nonrelativistic quantum mechanics and in relativistic quantum field theory, time t is a parameter and thus the time-reversal operator T does not actually reverse the sign of t. However, in relativistic quantum mechanics the time coordinate t and the space coordinates x are treated on an equal footing and all are operators. In this paper it is shown how to extend PT symmetry from nonrelativistic to relativistic quantum mechanics by implementing time reversal as an operation that changes the sign of the time coordinate operator t. Some illustrative relativistic quantum-mechanical models are constructed whose associated Hamiltonians are non-Hermitian but PT symmetric, and it is shown that for each such Hamiltonian the energy eigenvalues are all real.

18 pages, no figures

References in corpus (7)

• Making Sense of Non-Hermitian Hamiltonians
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• The ODE/IM Correspondence
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• Solution to the ghost problem in fourth order derivative theories
• PT symmetry and necessary and sufficient conditions for the reality of energy eigenvalues
• Giving up the ghost

Cited by in corpus (9)

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• Pseudo Hermitian Generalized Dirac Oscillators
• Spin-Vorticity Coupling for Massive Vector Mesons
• Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks
• A real expectation value of the time-dependent non-Hermitian Hamiltonians
• Reality from maximizing overlap in the periodic complex action theory
• Automatic hermiticity for mixed states
• A Generalized Uncertainty Principle from a Mediating Field