TY  - JOUR
A1  - Baumgaertel, Hellmut
T1  - Spectral and scattering theory of Friedrichs Models on the positive half line with Hilbert-Schmidt perturbations
N2  - The spectral theory of the Friedrichs model on the positive half line with Hilbert-Schmidt perturbations, equipped with distinguished analytic properties, is presented. In general, the (separable) multiplicity Hilbert space is assumed to be infinite-dimensional. The results include a spectral characterization of its resonances and the association of so-called Gamov vectors. Sufficient conditions are presented such that all resonances are simple poles of the scattering matrix. The connection between their residual terms and the associated Gamov vectors is pointed out.
Y1  - 2009
UR  - http://www.springerlink.com/content/105443
U6  - https://doi.org/10.1007/s00023-009-0398-8
SN  - 1424-0637
ER  - 
TY  - JOUR
A1  - Baumgaertel, Hellmut
A1  - Grundling, H.
T1  - Superselection in the presence of constraints
N2  - Superselection and constraints occur together in many gauge theories, and here we begin a study of such systems. Our main focus will be to analyze compatibility questions between constraining and superselection, and we will develop an example modelled on QED in which our framework is realized. We proceed from a generalization of Doplicher- Roberts superselection theory to the case of the nontrivial center, and a set of Dirac quantum constraints and find conditions under which the superselection structures will survive constraining in some form. This involves an analysis of the restriction and factorization of superselection structures. (c) 2005 American Institute of Physics
Y1  - 2005
SN  - 0022-2488
ER  - 
TY  - JOUR
A1  - Baumgaertel, Hellmut
A1  - Kaldass, Hani
A1  - Komy, Soliman
T1  - On spectral properties of the resonances for selected potential scattering systems
N2  - The resonances (poles of the scattering matrix) of quantum mechanical scattering by central-symmetric potentials with compact support and zero angular momentum are spectrally characterized directly in terms of the Hamiltonian by a (generalized) eigenvalue problem distinguished by an additional condition (called boundary condition). The connection between the (generalized) eigenspace of a resonance and corresponding Gamov vectors is pointed out. A condition is presented such that a relation between special transition probabilities and infinite sums of residual terms for all complex-conjugated pairs of resonances can be proved. In the case of the square well potential the condition is satisfied.
Y1  - 2009
UR  - http://jmp.aip.org/
U6  - https://doi.org/10.1063/1.3072675
SN  - 0022-2488
ER  -