CONTENTS -- Preface -- Zimmermann's Subtraction Scheme and the Perturbative Solution to the Renormalization Group Evolution Equations C. Becchi -- 1. Introduction -- 2. The renormalization group evolution equations -- 3. Comparison with Zimmermann's subtraction approach -- 4. Conclusions -- References -- A New Look at the Higgs-Kibble Model O. Steinmann -- 1. Introduction -- 2. The Model -- 3. Wightman Gauges -- 4. The Unitary Gauge -- 5. Renormalizability -- 6. The Non-Abelian Case -- References -- Large Regular QCD Coupling at Low Energy? D. V. Shirkov -- 1. The pQCD Overview -- 2. Analytic Perturbation Theory -- 2.1. APT - General -- 2.2. The APT Algorithm -- 2.3. APT functions at LE region -- 3. Low Energy APT Application -- 3.1. APT and bosonic spectrum -- 3.2. Bjorken sum rule -- 4. APT in QCD: Conclusion -- Acknowledgements -- References -- The Dihedral Group as a Family Group J. Kubo -- 1. Introduction -- 2. Finite groups -- 2.1. Character table -- 2.2. Tensor products -- 2.3. Finite groups of lower orders -- 3. The dihedral group -- 3.1. Matrix presentations of DN and Q2N -- 3.2. Irreducible representations of DN and QN -- 3.3. Tensor products -- 3.4. Q6 as an example -- 4. The model -- 4.1. Predictions -- 5. Zum Scluss -- References -- On the Consequences of Twisted Poincaré Symmetry Upon QFT on Moyal Noncommutative Spaces G. Fiore -- 1. Introduction -- 2. Twisting Poincaré group and Minkowski spacetime -- 3. Revisiting Wightman axioms for QFT and their consequences -- 4. Free or interacting scalar field -- 5. Conclusions. What do we learn? -- Acknowledgments -- References -- Taming the Landau Ghost in Noncommutative Quantum Field Theory H. Grosse -- 1. Preface -- 2. Introduction -- 3. Formulation of nc QFT on Moyal space -- 4. Renormalization -- 4.1. Matrix representation -- 4.2. The Polchinski equation for matrix models.

4.3. 4-theory on noncommutative R2 -- 4.4. 4-theory on noncommutative R4 -- 5. Taming the Landau ghost -- 6. Induced Gauge Theory -- 7. FERMIONS A spectral triple -- 8. Wedge-local QFT -- 9. Conclusion -- 10. Acknowledgments and Appendices -- References -- Warped Convolutions: A Novel Tool in the Construction of Quantum Field Theories D. Buchholz and S. J. Summers -- 1. Introduction -- 2. Warped convolutions -- 3. Deformations of quantum field theories -- 4. Concluding remarks -- References -- Quantum (or Averaged) Energy Inequalities in Quantum Field Theory R. Verch -- 1. Introduction -- 2. Quantum Fields on Curved Spacetime -- 3. Quantum Energy Inequalities -- 4. Local Thermal Equilibrium (LTE) States -- 5. Discussion -- References -- Field Theory and Brane Dynamics T. E. Clark -- 1. Introduction -- 2. Massive Brane Vectors -- 3. Collider Bounds On Brane Vector Parameter Space -- References -- Knots as Possible Excitations of the Quantum Yang-Mills Fields L. D. Faddeev -- 1. Dedication -- 2. Introduction -- 3. Nonlinear -model -- 4. Two component Landau-Ginzburg-Gross-Pitaevsky equation -- 5. SU(2) Yang-Mills theory -- References -- Feynman Graphs and Renormalization in Quantum Di usion L. Erd˝os, M. Salmhofer and H.-T. Yau -- 1. Introduction -- 2. The problem and the main result -- 3. Collision histories, Feynman graphs, and ladders -- 3.1. Collision histories -- 3.2. Disorder average and graphs -- 3.3. Graph bounds -- 3.4. Expansions to finite order and remainder terms -- 3.5. Long time scale: Renormalization -- 3.6. The key estimate for controlling combinatorics -- 4. Conclusion -- References -- Renormalization in Chaotic and Pseudochaotic Dynamical Systems J. H. Lowenstein -- 1. Introduction -- 2. Period-doubling cascade -- 2.1. Rayleigh-Bénard convection experiment -- 2.2. Logistic map -- 3. Chaotic and pseudochaotic kicked oscillators.

References -- Author Index.