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:
| [1] | DOI: 10.1016/0375-9474(87)90231-4 · doi:10.1016/0375-9474(87)90231-4 |
| [2] | DOI: 10.1103/PhysRevD.36.1465 · doi:10.1103/PhysRevD.36.1465 |
| [3] | DOI: 10.1088/0305-4470/20/12/022 · doi:10.1088/0305-4470/20/12/022 |
| [4] | DOI: 10.1063/1.528005 · Zbl 0658.47026 · doi:10.1063/1.528005 |
| [5] | DOI: 10.1063/1.528153 · Zbl 0657.46058 · doi:10.1063/1.528153 |
| [6] | DOI: 10.1215/S0012-7094-82-04901-8 · Zbl 0517.35026 · doi:10.1215/S0012-7094-82-04901-8 |
| [7] | DOI: 10.1103/PhysRevA.18.853 · doi:10.1103/PhysRevA.18.853 |
| [8] | DOI: 10.1016/0003-4916(77)90243-3 · doi:10.1016/0003-4916(77)90243-3 |
| [9] | DOI: 10.1007/BF01017937 · doi:10.1007/BF01017937 |
| [10] | Kerbikov B. O., Yad. Fiz. 41 pp 725– (1985) |
| [11] | DOI: 10.1103/PhysRevA.4.1782 · doi:10.1103/PhysRevA.4.1782 |
| [12] | DOI: 10.1103/PhysRevA.7.1288 · doi:10.1103/PhysRevA.7.1288 |
| [13] | DOI: 10.1016/0022-247X(81)90124-4 · Zbl 0473.47039 · doi:10.1016/0022-247X(81)90124-4 |
| [14] | DOI: 10.1103/PhysRevC.38.1076 · doi:10.1103/PhysRevC.38.1076 |
| [15] | DOI: 10.1007/BF01597446 · doi:10.1007/BF01597446 |
| [16] | Behncke N., Proc. Math. Soc. 72 pp 82– (1978) |
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