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Quantum Fields - Algebras, Processes

Are we living in a golden age? It is now more than half a century that Einstein and Heisenberg have given us the theories of relativity and of quantum mechanics, but the great challenge of 20th century science remains unre- solved: to assemble these building blocks into a fundamental theory of matter. And yet, for anyone watching the interplay of mathematics and theoretical physics to-day, developing symbiotically through the stimulus of a lively, even essential interdisciplinary dia- logue, this is a time of fascination and great satisfaction. It is also a time of gratitude to those who had the courage to in- sist that "a rudimentary knowledge of the Latin and Greek alpha- bets" was not enough, and tore down the barriers between the disciplines. On the basis of this groundwork there is now so much progress, and, notably, such strengthening of the dia].ogue with phenomenology that - reaching out for The Great Break- through - this may indeed turn out to be the golden age.
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Table of Contents

Causal Analysis in Terms of White Noise.- to Stochastic Differential Calculus.- A Generalized Stochastic Calculus in Homogenization.- Interaction Picture for Stochastic Differential Equations.- Path Integrals, Stationary Phase Approximations and Complex Histories.- Stochastic Dynamics and the Semiclassical Limit of Quantum Mechanics.- Asymptotic Expansion of Fresnel Integrals Relative to a Non-Singular Quadratic Form.- Scaling Limits of Generalized Random Processes.- Renormalization Group Analysis of Some Higly Bifurcated Families.- Anticommutative Integration and Fermi Fields.- Homogeneous Self-Dual Cones and Jordan Algebras.- Generators of One-Parameter Groups of *-Automorphisms on UHF-Algebras.- Automorphisms of Certain Simple C*-algebras.- Non-Commutative Group Duality and the Kubo-Martin-Schwinger Condition.- A Uniqueness Theorem for Central Extensions of Discrete Products of Cyclic Groups.- to W*-Categories.- Net Cohomology and Its Application to Field Theory.- Construction of Specifications.- On the Global Markov Property.- Uniqueness and Global Markov Property for Euclidean Fields and Lattice Systems.- Martingale Convergence and the Exponential Interaction in IR.- On Dia- and Paramagrietic Properties of Yang-Mills Potentials.- A New Look at Generalized, Non-Linear ?-Models and Yang-Mills Theory.- 1/N Expansions and the O(N) Nonlinear ?-Model in Two Dimensions.- On the z2 Lattice Higgs System.- Fluctuation of the Interface of the Two-Dimensional Ising Model.- The Stability Problem in ?4 Scalar Field Theories.- Summary.

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