Modified Spectral Boundary conditions in the Bag Model

TL;DR

This paper introduces a simplified, chirally invariant spectral boundary condition for the bag model, enabling Hamiltonian analysis of massless fermions in both Minkowski and Euclidean spaces.

Contribution

It presents a reduced form of spectral boundary conditions that are time-independent and chirally invariant, suitable for Hamiltonian studies of confined massless fermions.

Findings

Boundary conditions are chirally invariant and time-independent.

Applicable to both Minkowski and Euclidean space-times.

Facilitates Hamiltonian approach to chiral fermions in confined volumes.

Abstract

We propose a reduced form of Atiah-Patodi-Singer spectral boundary conditions for odd ($d$) dimensional spatial bag evolving in even ($d+1$) dimensional space-time. The modified boundary conditions are manifestly chirally invariant and do not depend on time. This allows to apply Hamiltonian approach to confined massless fermions and study chirality effects in spatially closed volume. The modified boundary conditions are equally suitable for chiral fermions in Minkowski and Euclidean metric space-times.