On the resolvent convergence of discrete Dirac operators on 3D cubic lattices

TL;DR

This paper proves that discrete Dirac operators on 3D cubic lattices converge to continuum Dirac operators in the strong resolvent sense, highlighting a specific mode of convergence.

Contribution

It establishes the strong resolvent convergence of discrete Dirac operators to their continuum counterparts in three dimensions, clarifying the nature of this convergence.

Findings

Discrete Dirac operators converge strongly to continuum operators.

Convergence does not hold in the norm resolvent sense.

Provides mathematical foundation for discretization of Dirac operators.

Abstract

We prove that the discrete Dirac operators in three dimensions converge to the continuum Dirac operators in the strong resolvent sense, but not in the norm resolvent sense.