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Full Description
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.
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.
