The magnetic formalism; new results

TL;DR

This paper reviews recent advances in magnetic pseudo-differential calculus, focusing on symbolic and $C^*$-algebraic approaches, and discusses applications to spectral analysis of operators with variable magnetic fields.

Contribution

It provides a comprehensive overview of recent developments in magnetic pseudo-differential calculus and explores their applications to spectral analysis.

Findings

Development of magnetic pseudo-differential calculus in symbolic form

Formulation of magnetic calculus in $C^*$-algebraic framework

Application to spectral analysis of variable magnetic field operators

Abstract

We review recent results on the magnetic pseudo-differential calculus both in symbolic and in $C^*$-algebraic form. We also indicate some applications to spectral analysis of pseudo-differential operators with variable magnetic fields.