Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra \cA \subeq C^\infty(M) which has to satisfy a non-degeneracy condition (the differentials of elements of \cA separate tangent vectors) and we postulate the existence of smooth Hamiltonian vector fields. Motivated by applications to Hamiltonian actions, we focus on affine Poisson spaces which include in particular the linear and affine Poisson structures on duals of locally convex Lie algebras. As an interesting byproduct of our approach, we can associate to an invariant symmetric bilinear form $\kappa$ on a Lie algebra \g and a $\kappa$-skew-symmetric derivation $D$ a weak affine Poisson structure on \g itself. This leads naturally to a concept of a Hamiltonian $G$-action on a weak Poisson manifold with a \g-valued momentum map and hence to a generalization of quasi-hamiltonian group actions

Closed forms and multi-moment maps

We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special holonomy. For forms of degree four, multi-moment maps are guaranteed to exist and are unique when the symmetry group is (3,4)-trivial, meaning that the group is connected and the third and fourth Lie algebra Betti numbers vanish. We give a structural description of some classes of (3,4)-trivial algebras and provide a number of examples.Comment: 36 page

An analogue of the Coleman-Mandula theorem for quantum field theory in curved spacetimes

The Coleman-Mandula (CM) theorem states that the Poincaré and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field theory in curved spacetimes, assuming local covariance, the timeslice property, a local dynamical form of Lorentz invariance, and additivity. Unlike the CM theorem, our result is valid in dimensions n≥2 and for free or interacting theories. It is formulated for theories defined on a category of all globally hyperbolic spacetimes equipped with a global coframe, on which the restricted Lorentz group acts, and makes use of a general analysis of symmetries induced by the action of a group G on the category of spacetimes. Such symmetries are shown to be canonically associated with a cohomology class in the second degree nonabelian cohomology of G with coefficients in the global gauge group of the theory. Our main result proves that the cohomology class is trivial if G is the universal cover S of the restricted Lorentz group. Among other consequences, it follows that the extended symmetry group is a direct product of the global gauge group and S, all fields transform in multiplets of S, fields of different spin do not mix under the extended group, and the occurrence of noninteger spin is controlled by the centre of the global gauge group. The general analysis is also applied to rigid scale covariance

Untersuchung zum Inventar und der Verteilung von 3H und 14C in abgebrannten SWR-Brennstaeben Abschlussbericht. Abschlussdatum: Oktober 1984

TIB: RO 2584 (1984,18) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Experimentelle Untersuchungen zum Verhalten des Iods bei hypothetischen Stoerfaellen Abschlussbericht. Abschlussdatum: Oktober 1985

TIB: RO 2584 (1985,7) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Spaltproduktfreisetzung Abschlussbericht. Beitrag zur Deutschen Risikostudie, Phase B

TIB: RO 2584 (1985,4) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Experimentelle Untersuchungen zur Abgabe von Spaltprodukten (insbesondere von Iod und Caesium) bei Auslegungsstoerfaellen Teilvorhaben 1. Abschlussbericht

TIB: RN 7995 (1984,008) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman