Projective Geometry and $\cal PT$-Symmetric Dirac Hamiltonian
High Energy Physics - Theory
2009-03-16 v2 Quantum Physics
Abstract
The -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 mass term is not Hermitian, but is invariant under the combined transformation of parity reflection and time reversal . When the symmetry is unbroken, the energy spectrum of the free spin- theory is real, with an appropriately shifted mass.
Cite
@article{arxiv.0901.2579,
title = {Projective Geometry and $\cal PT$-Symmetric Dirac Hamiltonian},
author = {Y. Jack Ng and H. van Dam},
journal= {arXiv preprint arXiv:0901.2579},
year = {2009}
}
Comments
7 pages, LaTeX; version accepted for publication in Phys. Lett. B; revised version incorporates useful suggestions from an anonymous referee