One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results

@article{Pankrashkin2014OnedimensionalDO,
  title={One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results},
  author={Konstantin Pankrashkin and S. Richard},
  journal={Journal of Mathematical Physics},
  year={2014},
  volume={55},
  pages={062305}
}
The spectral and scattering theory for 1-dimensional Dirac operators with mass $m$ and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new formulae take place in a representation which links, in a suitable way, the energies $-\infty$ and $+\infty$, and which emphasizes the role of $\pm m$. Finally, a topological version of Levinson's theorem is deduced, with the threshold effects at $\pm m… 
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