Projective Geometry and PT-Symmetric Dirac Hamiltonian
Feb, 2009Citations per year
Abstract: (Elsevier)
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 γ5 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- 12 theory is real, with an appropriately shifted mass.Note:
- 6 pages, LaTeX
- 02.40.Dr
- 03.65.Ta
- 03.65.-w
- parity: transformation
- dimension: 4
- energy spectrum
- Dirac equation
- time reversal
- PT symmetry
- geometry
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