Projective geometry and PT-symmetric Dirac Hamiltonian

@article{Ng2009ProjectiveGA,
title={Projective geometry and PT-symmetric Dirac Hamiltonian},
author={Y. J. Ng and H. V. Dam},
journal={Physics Letters B},
year={2009},
volume={673},
pages={237-239}
}

Abstract 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 P and time reversal T . When the PT symmetry is unbroken, the energy spectrum of the free spin- 1 2 theory is real, with an appropriately shifted mass.

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