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

TL;DR

This paper investigates the spectral behavior of Dirac-like operators with large mass terms on spin manifolds, revealing effective operators such as the extrinsic Dirac and a generalized MIT Bag operator, extending Euclidean results to general spin geometries.

Contribution

It introduces a generalized MIT Bag operator on spin manifolds and analyzes its spectral asymptotics in the non-relativistic limit, broadening the understanding beyond Euclidean spaces.

Findings

Spectral convergence to effective operators in large mass regimes

Extension of Euclidean results to general spin manifolds

Identification of a generalized MIT Bag operator in this context

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.