On Dirac operators with electrostatic δ-shell interactions of critical strength

2016/12/07 by Behrndt, Jussi, Holzmann, Markus
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1612.02290

Abstract

In this paper we prove that the Dirac operator A_η with an electrostatic δ-shell interaction of critical strength η= ± 2 supported on a C²-smooth compact surface Σ is self-adjoint in L²(ℝ³;ℂ⁴), we describe the domain explicitly in terms of traces and jump conditions in H^-1/2(Σ; ℂ⁴), and we investigate the spectral properties of A_η. While the non-critical interaction strengths η\not= ± 2 have received a lot of attention in the recent past, the critical case η= ± 2 remained open. Our approach is based on abstract techniques in extension theory of symmetric operators, in particular, boundary triples and their Weyl functions.

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