Pseudo-Bosons from Landau Levels

TL;DR

This paper constructs examples of pseudo-bosons derived from Landau level Hamiltonians in two dimensions and demonstrates limitations on generating pseudo-bosons through non-linear combinations of bosonic operators.

Contribution

It provides explicit constructions of pseudo-bosons from Landau levels and establishes a no-go theorem for non-linear bosonic operator combinations.

Findings

Pseudo-bosons can be constructed from Landau level Hamiltonians.

Non-linear combinations of bosonic operators cannot produce pseudo-bosons.

Abstract

We construct examples of pseudo-bosons in two dimensions arising from the Hamiltonian for the Landau levels. We also prove a no-go result showing that non-linear combinations of bosonic creation and annihilation operators cannot give rise to pseudo-bosons.