Absence of real resonances of Dirac operators

2025/05/20 by Henry Dumant, Dumant, Henry · 1 citation
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Algebraic and Geometric Analysis #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2505.14261

Abstract

The purpose of this paper is to introduce the resonances of Dirac operators by continuing meromorphically the truncated resolvent and to establish a result about their localization : a kind of Rellich Theorem. Firstly, we consider the case of the Dirac operator in an external field which is essentially bounded and compactly supported. Secondly, we consider the case of the MIT bag model outside a smooth and bounded obstacle.

Citations

• A strategy for self-adjointness of Dirac operators: Applications to the\n MIT bag model and delta-shell interactions
• Resonances for the radial Dirac operators
• Poisson wave trace formula for perturbed Dirac operators
• Resonances for 1D massless Dirac operators
• A class of analytic perturbations for one-body Schrödinger Hamiltonians

Cited by

• Dirac resonances as non-self-adjoint eigenvalues

Related

• Resonances for 1D massless Dirac operators
• Existence of Dirac resonances in the semi-classical limit
• Inverse resonance scattering for massless Dirac operators on the real line
• Resonances for the radial Dirac operators
• Resonances for Dirac operators on the half-line