# 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}
}
• Published 7 February 2014
• Mathematics, Physics
• Journal of Mathematical Physics
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 $\pm m… • Mathematics Revista Matemática Iberoamericana • 2022 In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it • Physics Journal of Physics A: Mathematical and Theoretical • 2023 In this paper the two-dimensional Dirac operator with a general hermitian δ-shell interaction supported on a straight line is introduced as a self-adjoint operator and its spectral properties are • Physics, Mathematics Journal of Mathematical Analysis and Applications • 2022 • Mathematics Reviews in Mathematical Physics • 2018 This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator • Physics Front. Phys. • 2019 We study the spectrum of the 1D Dirac Hamiltonian encompassing the bound and scattering states of a fermion distorted by a static background built from$\delta\$-function potentials. After introducing
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