Eigenvalue Curves for Generalized MIT Bag Models

This is a post-peer-review, pre-copyedit version of an article published in Communications in Mathematical Physics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00220-022-04526-3 ; We study spectral properties of Dirac operators on bounded domains Ω ⊂ R3 with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter τ∈ R; the case τ= 0 corresponds to the MIT bag model. We show that the eigenvalues are parametrized as increasing functions of τ, and we exploit this monotonicity to study the limits as τ→ ± ∞. We prove that if Ω is not a ball then the first positive eigenvalue is greater than the one of a ball with the same volume for all τ large enough. Moreover, we show that the first positive eigenvalue converges to the mass of the particle as τ↓ - ∞, and we also analyze its first order asymptotics ; ERC-2014-ADG project HADE Id. 669689 (European Research Council), PGC2018-094522-B-I00, MTM2017-84214-C2-1-P, RED2018-102650-T, SEV-2017-0718