A vanishing theorem for operators in Fock space

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.Comment: 14 page

The three-form multiplet in N=2 superspace

We present an N=2 multiplet including a three-index antisymmetric tensor gauge potential, and describe it as a solution to the Bianchi identities for the associated fieldstrength superform, subject to some covariant constraints, in extended central charge superspace. We find that this solution is given in terms of an 8+8 tensor multiplet subject to an additional constraint. We give the transformation laws for the multiplet as well as invariant superfield and component field lagrangians, and mention possible couplings to other multiplets. We also allude to the relevance of the 3--form geometry for generic invariant supergravity actions.Comment: 12 pages, LaTeX (2.09). (Final version to appear in Z.Phys.C

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of $\alpha^{3/2}$, $\alpha$ being the fine structure constant. A suitably chosen ground state vector depends analytically on $\alpha^{3/2}$ and it is twice continuously differentiable with respect to the nuclear coordinates.Comment: 47 page

Smoothness and analyticity of perturbation expansions in QED

We consider the ground state of an atom in the framework of non-relativistic qed. We assume that the ultraviolet cutoff is of the order of the Rydberg energy and that the atomic Hamiltonian has a non-degenerate ground state. We show that the ground state energy and the ground state are k-times continuously differentiable functions of the fine structure constant and respectively the square root of the fine structure constant on some nonempty interval [0,c_k).Comment: 53 page