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181
CONTINUOUS BOUNDED COHOMOLOGY AND APPLICATIONS TO RIGIDITY THEORY
 GAFA GEOMETRIC AND FUNCTIONAL ANALYSIS
, 2002
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Construction of Quantum Field Theories with Factorizing SMatrices
, 2007
"... A new approach to the construction of interacting quantum field theories on twodimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing Smatrix in two steps. At first, quantum fields which are localized in infinitely extended, wedgeshaped region ..."
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Cited by 68 (9 self)
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A new approach to the construction of interacting quantum field theories on twodimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing Smatrix in two steps. At first, quantum fields which are localized in infinitely extended, wedgeshaped regions of Minkowski space are constructed explicitly. In the second step, local observables are analyzed with operatoralgebraic techniques, in particular by using the modular nuclearity condition of Buchholz, d’Antoni and Longo. Besides a modelindependent result regarding the ReehSchlieder property of the vacuum in this framework, an infinite class of quantum field theoretic models with nontrivial interaction is constructed. This construction completes a program initiated by Schroer in a large family of theories, a particular example being the SinhGordon model. The crucial problem of establishing the existence of local observables in these models is solved by verifying the modular nuclearity condition, which here amounts to a condition on analytic properties of form factors of observables localized in wedge regions. It is shown that the constructed models solve the inverse scattering problem for the considered class of Smatrices. Moreover, a proof of asymptotic completeness is obtained by explicitly computing total sets of scattering states. The structure of these collision states is found to be in agreement with the heuristic formulae underlying the ZamolodchikovFaddeev algebra.
On Köthe sequence spaces and linear logic
 Mathematical Structures in Computer Science
, 2001
"... We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Kothe sequence spaces. In this setting, the spaces interpreting the exponential have a quite simple structure of commutative Hopf algebra. The ..."
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Cited by 41 (12 self)
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We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Kothe sequence spaces. In this setting, the spaces interpreting the exponential have a quite simple structure of commutative Hopf algebra. The coKleisli category of this linear category is a cartesian closed category of entire mappings. This work provides a simple setting where typed calculus and dierential calculus can be combined; we give a few examples of computations. 1
Particle weights and their disintegration I
"... The notion of Wigner particles is attached to irreducible unitary representations of the Poincaré group, characterized by parameters m and s of mass and spin, respectively. However, the Lorentz symmetry is broken in theories with longrange interactions, rendering this approach inapplicable (infrapa ..."
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Cited by 25 (1 self)
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The notion of Wigner particles is attached to irreducible unitary representations of the Poincaré group, characterized by parameters m and s of mass and spin, respectively. However, the Lorentz symmetry is broken in theories with longrange interactions, rendering this approach inapplicable (infraparticle problem). A unified treatment of both particles and infraparticles via the concept of particle weights can be given within the framework of local quantum physics. They arise as temporal limits of physical states in the vacuum sector and describe the asymptotic particle content. In this paper their definition and characteristic properties, already presented in [9] and [14], are worked out in detail. The existence of the temporal limits is established by use of suitably defined seminorms which are also essential in proving the characteristic features of particle weights. 1
Full asymptotic expansion of the heat trace for non–self–adjoint . . .
, 2001
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A convenient differential category
, 2011
"... We show that the category of convenient vector spaces in the sense of Frölicher ..."
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Cited by 19 (2 self)
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We show that the category of convenient vector spaces in the sense of Frölicher
T.Rybicki, On the Group of Diffeomorphisms Preserving a Locally Conformal Symplectic Structure
 Ann. Global Anal. and Geom
, 1999
"... Abstract. The automorphism group of a locally conformal symplectic structure is studied. It is shown that this group possesses essential features of the symplectomorphism group. By using a special type of cohomology the flux and Calabi homomorphisms are introduced. The main theorem states that the ..."
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Cited by 19 (4 self)
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Abstract. The automorphism group of a locally conformal symplectic structure is studied. It is shown that this group possesses essential features of the symplectomorphism group. By using a special type of cohomology the flux and Calabi homomorphisms are introduced. The main theorem states that the kernels of these homomorphisms are simple groups, for the precise statement see chapter 7. Some of the methods used, may also be interesting in the symplectic case.
The ReehSchlieder property for quantum fields on stationary spacetimes”, mathph/0002054
"... We show that as soon as a linear quantum field on a stationary spacetime satisfies a certain type of hyperbolic equation, the (quasifree) ground and KMSstates with respect to the canonical time flow have the ReehSchlieder property. We also obtain an analog of Borchers ’ timelike tube theorem. The ..."
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Cited by 18 (3 self)
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We show that as soon as a linear quantum field on a stationary spacetime satisfies a certain type of hyperbolic equation, the (quasifree) ground and KMSstates with respect to the canonical time flow have the ReehSchlieder property. We also obtain an analog of Borchers ’ timelike tube theorem. The class of fields we consider contains the Dirac field, the KleinGordon field and the Proca field.
Aspects of the theory of infinite dimensional manifolds
 Differential Geometry and Applications 1
, 1991
"... Abstract. The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent vectors as derivations. Manifolds of mappings and dif ..."
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Cited by 18 (11 self)
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Abstract. The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent vectors as derivations. Manifolds of mappings and diffeomorphisms are treated. Finally the differential structure on the inductive limits of the groups GL(n), SO(n) and some of their homogeneus spaces is treated.
Direct limits of infinitedimensional Lie groups compared to direct limits in related categories
 J. Funct. Anal
, 2007
"... Let G be a Lie group which is the union of an ascending sequence G1 ⊆ G2 ⊆ · · · of Lie groups (all of which may be infinitedimensional). We study the question when G = lim Gn in the category of Lie groups, topological groups, smooth manifolds, resp., topological spaces. Full answers are obtaine ..."
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Cited by 17 (6 self)
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Let G be a Lie group which is the union of an ascending sequence G1 ⊆ G2 ⊆ · · · of Lie groups (all of which may be infinitedimensional). We study the question when G = lim Gn in the category of Lie groups, topological groups, smooth manifolds, resp., topological spaces. Full answers are obtained for G the group Diffc(M) of compactly supported C∞diffeomorphisms of a σcompact smooth manifold M; and for test function groups C ∞ c (M,H) of compactly supported smooth maps with values in a finitedimensional Lie group H. We also discuss the cases where G is a direct limit of unit groups of Banach algebras, a Lie group of germs of Lie groupvalued analytic maps, or a weak direct product of Lie groups.