Dirac-like operators on the Hilbert space of differential forms on manifolds with boundaries

Abstract

The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like potentials, in manifolds of dimension higher than one. Self-adjoint boundary conditions for the case of dimension 2 are obtained explicitly.

References in corpus (2)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Self-adjointness of Dirac operators via Hardy-Dirac inequalities

Cited by in corpus (5)

• Finite element method to solve the spectral problem for arbitrary self-adjoint extensions of the Laplace-Beltrami operator on manifolds with a boundary
• On $\mathbb{Z}$-invariant self-adjoint extensions of the Laplacian on quantum circuits
• Representation of non-semibounded quadratic forms and orthogonal additivity
• Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions
• On a sharper bound on the stability of non-autonomous Schrödinger equations and applications to quantum control