A vanishing theorem for operators in Fock space

TL;DR

This paper proves a vanishing theorem for certain rotation-invariant operators in bosonic Fock space, showing they cannot create or annihilate a single particle, with applications to Hamiltonian analysis in non-relativistic quantum electrodynamics.

Contribution

It establishes a new vanishing theorem linking rotation invariance to particle creation and annihilation operators in Fock space.

Findings

Rotation invariance implies the absence of single-particle creation or annihilation terms.

The result has applications in operator theoretic renormalization of Hamiltonians in non-relativistic QED.

Provides a mathematical tool for analyzing symmetries in quantum field operators.

Abstract

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that rotation invariance implies the absence of terms which either create or annihilate only a single particle. We outline an application of this result in an operator theoretic renormalization analysis of Hamilton operators, which occur in non-relativistic qed.