Ebook: 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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Content:
Front Matter....Pages I-IX
Causal Analysis in Terms of White Noise....Pages 1-19
Introduction to Stochastic Differential Calculus....Pages 21-40
A Generalized Stochastic Calculus in Homogenization....Pages 41-51
Interaction Picture for Stochastic Differential Equations....Pages 53-64
Path Integrals, Stationary Phase Approximations and Complex Histories....Pages 65-78
Stochastic Dynamics and the Semiclassical Limit of Quantum Mechanics....Pages 79-90
Asymptotic Expansion of Fresnel Integrals Relative to a Non-Singular Quadratic Form....Pages 91-106
Scaling Limits of Generalized Random Processes....Pages 107-124
Renormalization Group Analysis of Some Highly Bifurcated Families....Pages 125-134
Anticommutative Integration and Fermi Fields....Pages 135-151
Homogeneous Self-Dual Cones and Jordan Algebras....Pages 153-165
Generators of One-Parameter Groups of *-Automorphisms on UHF-Algebras....Pages 167-185
Automorphisms of Certain Simple C*-algebras....Pages 187-196
Non-Commutative Group Duality and the Kubo-Martin-Schwinger Condition....Pages 197-205
A Uniqueness Theorem for Central Extensions of Discrete Products of Cyclic Groups....Pages 207-221
Introduction to W*-Categories....Pages 223-238
Net Cohomology and Its Applications to Field Theory....Pages 239-268
Construction of Specifications....Pages 269-292
On the Global Markov Property....Pages 293-302
Uniqueness and Global Markov Property for Euclidean Fields and Lattice Systems....Pages 303-329
On Dia- and Paramagnetic Properties of Yang-Mills Potentials....Pages 331-353
A New Look at Generalized, Non-Linear ?-Models and Yang-Mills Theory....Pages 355-360
1/N Expansions and the O(N) Nonlinear ?-Model in Two Dimensions....Pages 361-378
On the ?2 Lattice Higgs System....Pages 379-382
Fluctuation of the Interface of the Two-Dimensional Ising Model....Pages 383-395
The Stability Problem in ф4 Scalar Field Theories....Pages 397-405
Summary....Pages 407-440
....Pages 441-444