Dirac operators with a spherically symmetric \(\delta\)-shell interaction. (English) Zbl 0694.46053
Summary: Dirac operators with a contact interaction supported by a sphere are studied restricting attention to the operators that are rationally and space-reflection symmetric. The partial wave operators are constructed using the selfadjoint extension theory, a particular attention being paid to those among them that can be interpreted as \(\delta\)-function shells of scalar and vector nature. The class of interactions for which the sphere becomes impenetrable is specified and spectral properties of the obtained Hamiltonians are discussed.
MSC:
46N99 | Miscellaneous applications of functional analysis |
47A20 | Dilations, extensions, compressions of linear operators |
47E05 | General theory of ordinary differential operators |
47A10 | Spectrum, resolvent |
47A40 | Scattering theory of linear operators |
Keywords:
Dirac operators with a contact interaction supported by a sphere; partial wave operators; selfadjoint extension theory; spectral propertiesReferences:
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