A generalized MIT Bag operator on spin manifolds in the non-relativistic limit

Abstract

We consider Dirac-like operators with piecewise constant mass terms on spin manifolds, and we study the behaviour of their spectra when the mass parameters become large. In several asymptotic regimes, effective operators appear: the extrinsic Dirac operator and a generalized MIT Bag Dirac operator. This extends some results previously known for the Euclidean spaces to the case of general spin geometry. Contents 1. Introduction 1 2. Notations and preliminaries. 6 3. Definition of the operators 13 4. Sesquilinear forms for the operators with mass 18 5. Operators in tubular coordinates 25 6. Analysis of the one-dimensional operators 31 7. Asymptotics analysis for the operator A m 33 8. The operator B 2 m,M in the limit of large M 37 9. The operator B m,M for large masses 41 References 44