A vanishing theorem for operators in Fock space
arXiv:1107.4577 · doi:10.1007/s11005-012-0567-4
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.
14 pages