TY - JOUR A1 - Baumgärtel, Hellmut T1 - A Characteristic decay semigroup for the resonances of trace class perturbations with analyticity conditions of semibounded hamiltonians JF - International journal of theoretical physic N2 - To asymptotic complete scattering systems {M(+) + V, M(+)} on H(+) := L(2)(R(+), K, d lambda), where M(+) is the multiplication operator on H(+) and V is a trace class operator with analyticity conditions, a decay semigroup is associated such that the spectrum of the generator of this semigroup coincides with the set of all resonances (poles of the analytic continuation of the scattering matrix into the lower half plane across the positive half line), i.e. the decay semigroup yields a "time-dependent" characterization of the resonances. As a counterpart a "spectral characterization" is mentioned which is due to the "eigenvalue-like" properties of resonances. KW - Resonances KW - Scattering theory KW - Lax-Phillips theory KW - Decay semigroups Y1 - 2011 U6 - https://doi.org/10.1007/s10773-010-0533-9 SN - 0020-7748 VL - 50 IS - 7 SP - 2002 EP - 2008 PB - Springer CY - New York ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - A modified approach to the Doplicher-Roberts theorem on the construction of field algebra and the symmetry group in superselection theory T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik Y1 - 1994 VL - 134 CY - Berlin ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - A modified approach to the Doplicher-Roberts theorem on the construction of the field algebra and the symmetry group in superselection theory Y1 - 1997 ER - TY - BOOK A1 - Baumgärtel, Hellmut A1 - Jurke, Matthias A1 - Lledó, Fernando T1 - A remark on covariant and causal nets of CAR-resp.CCR-type local algebras assigned to the irreducible unitary representation of the poincare group labeled by (m>0, s, +) T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik Y1 - 1994 VL - 120 CY - Berlin ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Actions of finite abelian groups on abelian C*-algebras Z: Second cohomology and description by C*-extensions F ) Z T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik Y1 - 1999 VL - 383 CY - Berlin ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - An Application of the DR-Duality Theory for Compact Groups to Endomorphism Categories of C*-Algebras with Nontrivial Center Y1 - 2001 ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - An inverse problem for superselection structures on C*-algebras with nontrivial center Y1 - 1999 ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Betrachtungen zur kulturellen Dimension der Mathematik T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1997 VL - 1997, 15 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Cuntz algebras and superselection structures in Quantum Field Theory T3 - LQP Papers / Local Quantum Physics Crossroads Y1 - 1999 UR - http://www.lqp.uni-goettingen.de PB - Univ. CY - Göttingen ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - Dual actions on C*-algebras and Hilbert extensions Y1 - 2000 ER - TY - BOOK A1 - Baumgärtel, Hellmut A1 - Lledó, Fernando T1 - Dual group actions on C*-algebras and their description by Hilbert extensions T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik Y1 - 2000 VL - 445 PB - Techn. Univ. CY - Berlin ER - TY - JOUR A1 - Baumgärtel, Hellmut A1 - Lledo, Fernando T1 - Duality of compact groups and Hilbert C*-systems for C*-algebras with a nontrivial center N2 - In this paper we present duality theory for compact groups in the case when the C*-algebra A, the fixed point algebra of the corresponding Hilbert C*-system (F, 9), has a nontrivial center Z superset of C1 and the relative commutant satisfies the minimality condition A' boolean AND F = Z, as well as a technical condition called regularity. The abstract characterization of the mentioned Hilbert C*-system is expressed by means of an inclusion of C*- categories T-c < T, where T-c is a suitable DR-category and T a full subcategory of the category of endomorphisms of A. Both categories have the same objects and the arrows of T can be generated from the arrows of T-c and the center Z. A crucial new element that appears in the present analysis is an abelian group C(G), which we call the chain group of G, and that can be constructed from certain equivalence relation defined on (G) over cap, the dual object of G. The chain group, which is isomorphic to the character group of the center of g, determines the action of irreducible endomorphisms of A when restricted to Z. Moreover, C(g) encodes the possibility of defining a symmetry epsilon also for the larger category T of the previous inclusion Y1 - 2004 SN - 0129-167X ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - Erhard Schmidt, John von Neumann Y1 - 1998 SN - 3-7643-5943- 9 ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - Fourier transformation of Hilbert C*-systems, with compact groups, by their regular representation Y1 - 1995 ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - Generalized eigenvectors for resonances in the Friedrichs model and their associated Gamov vectors N2 - A Gelfand triplet for the Hamiltonian H of the Priedrichs model on R with multiplicity space K, dim K < infinity, is constructed such that exactly the resonances (poles of the inverse of the Livsic-matrix) are (generalized) eigenvalues of H. The corresponding eigen(anti)linear forms are calculated explicitly. Using the wave matrices for the wave (Moller) operators the corresponding eigen(anti)linear forms on the Schwartz space S for the unperturbed Hamiltonian Ho are also calculated. It turns out that they are of pure Dirac type and can be characterized by their corresponding Gamov vector lambda -> k/(zeta(0)-lambda)(-1), zeta(0) resonance, k epsilon K, which is uniquely determined by restriction of S to S boolean AND H-+(2), where H-+(2) denotes the Hardy space of the upper half-plane. Simultaneously this restriction yields a truncation of the generalized evolution to the well-known decay semigroup for t >= 0 of the Toeplitz type on H-+(2). That is: Exactly those pre-Gamov vectors a lambda -> k/(zeta-lambda)(-1), ( from the lower half-plane, k epsilon K., have an extension to a generalized eigenvector of H if zeta is a resonance and if k is from that subspace of K which is uniquely determined by its corresponding Dirac type antilinear form Y1 - 2006 UR - http://www.worldscinet.com/rmp/rmp.shtml U6 - https://doi.org/10.1142/S0129055X06002589 SN - 0129-055X ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Group actions on C*-algebras and their description by Hilbert C*-extensions T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik Y1 - 1999 VL - 385 CY - Berlin ER - TY - JOUR A1 - Baumgärtel, Hellmut A1 - Carey, A. T1 - Hilbert systems for actions of the circle group Y1 - 2001 ER - TY - BOOK A1 - Baumgärtel, Hellmut A1 - Carey, A. T1 - Hilbert systems for actions of the circle group T3 - ESI-Preprint / Erwin-Schröder-Institut für Mathematische Physik, Wien Y1 - 2000 VL - 940, 2000 PB - Erwin-Schröder-Institut für Mathematische Physik CY - Wien ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - Laudatio Hans Kaiser Y1 - 1993 ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - Lax-phillips evolutions in quantum mechanics and two-space scattering Y1 - 2004 SN - 0034-4877 ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - Lax-phillips evolutions in quantum mechanics and two-space scattering Y1 - 2004 SN - 0034-4877 ER - TY - BOOK A1 - Baumgärtel, Hellmut A1 - Jurke, Matthias A1 - Lledó, Fernando T1 - Mathematische Strukturen passen auf die Natur : Reflexionen über das Wechselverhältnis von Mathematik und Physik T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 18 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - On a critical radiation density in the Friedmann equation JF - Journal of mathematical physics N2 - The paper presents a classification of the basic types of admissible solutions of the general Friedmann equation with non-vanishing cosmological constant and for the case that radiation and matter do not couple. There are four distinct types. The classification uses first the discriminant of a polynomial of the third degree, closely related to the right hand side of the Friedmann equation. The decisive term is then a critical radiation density which can be calculated explicitly. Y1 - 2012 U6 - https://doi.org/10.1063/1.4771668 SN - 0022-2488 VL - 53 IS - 12 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - On a theorem of Ashtekar and Lewandowski Y1 - 1999 SN - 981-023627-1 ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - On a theorem of Ashtekar and Lewandowski in the mathematical framework of canonical quantization in quantum gravity Y1 - 2000 ER - TY - JOUR A1 - Baumgärtel, Hellmut A1 - Jurke, Matthias A1 - Lledó, Fernando T1 - On free nets over Minkowski space Y1 - 1995 ER - TY - JOUR A1 - Baumgärtel, Hellmut T1 - On Haag dual nets over compact spaces Y1 - 1995 ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Operatoralgebraic methods in quantum field theory : a series of lectures Y1 - 1995 PB - Akademie Verl. CY - Berlin ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Operatoralgebren und Quantenfeldtheorie T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1993 VL - 1993, 12 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Some operatoralgebraic fundamentals of the algebraic quantum field theory T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1993 VL - 1993, 09 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Baumgärtel, Hellmut A1 - Lledó, Fernando T1 - Some results on superselection structures for C*-algebras with nontrivial center Y1 - 1997 SN - 981-02-3984-X ER - TY - JOUR A1 - Baumgärtel, Hellmut A1 - Lledó, Fernando T1 - Superselection structures for C*-algebras with nontrivial center Y1 - 1997 ER - TY - BOOK A1 - Baumgärtel, Hellmut A1 - Jurke, Matthias A1 - Lledó, Fernando T1 - Symmetrie und Quantentheorie T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1995 VL - 1995, 6 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Baumgärtel, Hellmut A1 - Jurke, Matthias A1 - Lledó, Fernando T1 - Twisted duality for the CAR-algebra Y1 - 2002 ER - TY - BOOK A1 - Baumgärtel, Hellmut A1 - Jurke, Matthias A1 - Lledó, Fernando T1 - Twisted duality for the CAR-algebra T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik Y1 - 1999 UR - http://www-sfb288.math.tu-berlin.de/Publications/Preprints.html VL - 401 PB - Techn. Univ. CY - Berlin ER - TY - BOOK A1 - Baumgärtel, Hellmut T1 - Über Superauswahlstrukturen und deren Eichgruppen T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1997 VL - 1997, 06 PB - Univ. CY - Potsdam ER -