The integral form of APS boundary conditions in the Bag Model

TL;DR

This paper introduces an integral formulation of APS boundary conditions in the Bag Model, explicitly constructs the projector for a spherical cavity, and discusses its universal relation with the fermion propagator across dimensions.

Contribution

It presents a new integral form of APS boundary conditions and explicitly derives the projector for spherical cavities, extending their applicability.

Findings

Explicit integral projector for spherical cavity boundary conditions

Universal relation between projector and fermion propagator

Applicability across different bag forms and space dimensions

Abstract

We propose an integral form of Atiah-Patodi-Singer spectral boundary conditions (SBC) and find explicitly the integral projector onto SBC for the 3-dimensional spherical cavity. After discussion of a simple example we argue that the relation between the projector and fermion propagator is universal and stays valid independently of the bag form and space dimension.