9,052 research outputs found
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
, being the fine structure constant. A suitably chosen
ground state vector depends analytically on 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
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