Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory Proceedings of the Colloquium Held at Les Houches, Centre de Physique September 1979

Essential support theory and u=0 theorems.- The theory of holonomic systems with regular singularities and its relevance to physical problems.- Second-microlocalization and asymptotic expansions.- Deuxieme microlocalisation.- Sur le problème de Hilbert-Riemann.- Conditions de positivité dans une variété symplectique complexe . Applications à l'étude des microfonctions.- Fuchsian systems of linear differential equations associated to Nilsson class functions and an application to Feynman integrals.- Singularites des solutions des equations aux derivees partielles non linearies.- Comportement semi classique du spectre d'un hamiltonien quantique.- Rational and Padé approximations to solutions of linear differential equations and the monodromy theory.- METHODE DE LA PHASE STATIONNAIRE ET SOMMATION DE BOREL.- Les series ? — sommables et leurs applications.- Reflection of analytic singularities.- Les operateurs metadifferentiels.- Asymptotic behaviour of Feynman integrals.- Integral relations in complex space and the global analytic and monodromic structure of Green's functions in quantum field theory: Some general ideas and recent results.- Microcausality, macrocasuality and the physical region (micro)analytic S-matrix.- Analytic 2-particle structure and crossing constraints.- On the scattering matrix with indefinite metric.- On the representation of the local current algebra.- S matrix theory of the massive thirring model.- Field theories in 1+1-dimensions with soliton behaviour: Form factors and Green's functions.- One and multidimensional completely integrable systems arising from the isospectral deformation.- Quantization of exactly integrable field theoretic models.- Aspects of Holonomic quantum fields.- Recent results for the planar Ising model.