Eigenvalue Boundary Problems for the Dirac Operator

The Dirac System on the Anti-de Sitter Universe

“…Therefore, in the massless case, we deal with a classical mixed hyperbolic problem, and different boundary conditions for the Dirac system with regular potential are well known (see e.g. [5], [6], [9], [10], [16], [20]). We recall an important local boundary condition for the Dirac spinors defined on some open domain Ω of the space-time, the so called generalized MIT-bag condition :…”

“…The gravitational potential plays the role of a variable mass that tends to the infinity at the space infinity ; the rather similar Dirac equation on Minkowski space with increasing potential has been considered in [23], [34], [38]. The litterature on the boundary value problems for the Dirac system is huge ; among important contributions, we can cite [5], [6], [9], [10], [16], [20]. There are few papers concerning the deep problem of the global existence of fields on the non-globally hyperbolic lorentzian manifolds, in particular [2], [11], [13], [21], [22], [32].…”

Eigenvalue estimates for the Dirac operator with generalized APS boundary condition

“…Since the spinor field ϕ + γ(e 0 )ϕ is an eigenspinor of D with a eigenvalue − In particular, if we take b = 0, the above theorem is exactly the Theorem 5 in [15].…”

“…From [14] or [15], one gets the integral form of the Schrödinger-Lichnerowicz formula for a compact Riemannian spin manifold with compact boundary…”

Green functions for the Dirac operator under local boundary conditions and applications

“…We first begin with a brief introduction on this invariant. We have seen in Section 3.1 (see [HMR02] for more details) that the spectrum of the Dirac operator under the chiral bag boundary condition consists of entirely isolated real eigenvalues with finite multiplicity. If we denote by λ ± 1 (g) the first eigenvalue of the Dirac operator D g under the boundary condition B ± CHI , then the chiral bag invariant is defined by:…”