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66
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 31 (9 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
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 21 (5 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.
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.
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 12 (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.
The Convenient Setting For Real Analytic Mappings
 ACTA MATHEMATICA
, 1990
"... We present here ”the” cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps smooth curves to smooth curves and real analytic curves to real analytic curves. Under mild completenes ..."
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Cited by 11 (10 self)
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We present here ”the” cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps smooth curves to smooth curves and real analytic curves to real analytic curves. Under mild completeness conditions the second requirement can be replaced by: real analytic along affine lines. Enclosed and necessary is a careful study of locally convex topologies on spaces of real analytic mappings. As an application we also present the theory of manifolds of real analytic mappings: the group of real analytic diffeomorphisms of a compact real analytic manifold is a real analytic Lie group.
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 10 (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
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 7 (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.
Local properties of accessible injective operator ideals
 Czech. Math. Journal
, 1998
"... In addition to Pisier’s counterexample of a nonaccessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a ”good behaviour ” of trace duality, which is canonically induced by conjugate operator ideals ..."
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Cited by 6 (5 self)
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In addition to Pisier’s counterexample of a nonaccessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a ”good behaviour ” of trace duality, which is canonically induced by conjugate operator ideals can be extended to adjoint Banach ideals, if and only if these adjoint ideals satisfy an accessibility condition (theorem 3.1). This observation leads in a natural way to a characterization of accessible injective Banach ideals, where we also recognize the appearance of the ideal of absolutely summing operators (prop. 4.1). By the famous Grothendieck inequality, every operator from L1 to a Hilbert space is absolutely summing, and therefore our search for such ideals will be directed towards Hilbert space factorization via an operator version of Grothendieck’s inequality (lemma 4.2). As a consequence, we obtain a class of injective ideals, which are ”quasiaccessible”, and with the help of tensor stability, we improve the corresponding norm inequalities, to get accessibility (theorem 4.1 and 4.2). In the last chapter of this paper we give applications, which are implied by a nontrivial link of the above mentioned considerations to normed products of operator ideals. Key words and phrases: accessibility, Banach spaces, conjugate operator ideals, Hilbert space factorization, Grothendieck’s inequality, tensor norms, tensor stability
PHASE SPACE PROPERTIES OF CHARGED FIELDS IN THEORIES OF LOCAL OBSERVABLES
, 1994
"... Within the setting of algebraic quantum field theory a relation between phasespace properties of observables and charged fields is established. These properties are expressed in terms of compactness and nuclearity conditions which are the basis for the characterization of theories with physically r ..."
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Cited by 6 (1 self)
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Within the setting of algebraic quantum field theory a relation between phasespace properties of observables and charged fields is established. These properties are expressed in terms of compactness and nuclearity conditions which are the basis for the characterization of theories with physically reasonable causal and thermal features. Relevant concepts and results of phase space analysis in algebraic quantum field theory are reviewed and the underlying ideas are outlined.