Physics

Dirac algebra

Dirac spinor

Operator (biology)

Resolvent

Mathematics

Mathematical physics

Compact operator

Transcription factor

Gene

Dirac measure

Ladder operator

Dirac operator

Momentum operator

Mathematical analysis

Political science

Neutrino

Repressor

Chemistry

Programming language

Geometry

Extension (predicate logic)

Computer science

Dirac (video compression format)

Quantum mechanics

Dirac equation

Biochemistry

Scalar (mathematics)

Unitary state

Revista Matemática Iberoamericana

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 into a linear combination of four elementary interactions: electrostatic, Lorentz scalar, magnetic, and a fourth one which can be absorbed by using unitary transformations. We address the self-adjointness and the spectral description of the underlying Dirac operator. In the non-critical case, we do so by providing a boundary triple, and in the critical purely magnetic case, by exploiting the phenomenon of confinement and super-symmetry. Moreover, we justify our model by showing that Dirac operators with singular interactions are limits in the strong resolvent sense of Dirac operators with regular potentials.

General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation