Ebook: New Developments in Quantum Field Theory and Statistical Mechanics Cargèse 1976

The 1976 Cargese Summer Institute was devoted to the study of certain exciting developments in quantum field theory and critical phenomena. Its genesis occurred in 1974 as an outgrowth of many scientific discussions amongst the undersigned, who decided to form a scientific committee for the organization of the school. On the one hand, various workers in quantum field theory were continuing to make startling progress in different directions. On the other hand, many new problems were arising from these various domains. Thus we feIt that 1976 might be an appropriate occasion both to review recent developments and to encourage interactions between researchers from different backgrounds working on a common set of unsolved problems. An important aspect of the school, as it took place, was the participation of and stimulating interaction between such a broad spectrum of theorists. The central topics of the school were chosen from the areas of solitons, phase transitions, critical behavior, the renormalization group, gauge fields and the analysis of nonrenormalizable field theories. A noteworthy feature of these topics is the interpene­ tration of ideas from quantum field theory and statistical mechanics whose inherent unity is seen in the functional integral formulation of quantum field theory. The actual lectures were partly in the form of tutorials designed to familiarize the participants with re­ cent progress on the main topics of the school. Others were in the form of more specialized seminars reporting on recent research.

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Content:
Front Matter....Pages i-x
A Tutorial Course in Constructive Field Theory....Pages 1-34
Functional Integral Methods in Quantum Field Theory....Pages 35-66
How to Parametrize the Solutions of Lagrangian Field Theories: Symmetry Breaking, and Dimensional Interpolation and Renormalization in the (ϕ4)n Model....Pages 67-77
Phase Transitions in Statistical Mechanics and Quantum Field Theory....Pages 79-130
Continuous Symmetry Breakdown in 2+ε Dimension: The Non-Linear σ Model....Pages 131-142
Quantum Chromodynamics on a Lattice....Pages 143-172
Gauge Theories on the Lattice....Pages 173-199
Continuum Gauge Theories....Pages 201-224
Massless Renormalizable Field Theories and the Yang-Mills Field....Pages 225-239
Conformal Invariant Quantum Field Theory....Pages 241-264
Regularized Quantum Field Theory....Pages 265-279
On Non-Renormalizable Interactions....Pages 281-305
The Classical Sine Gordon Theory....Pages 307-338
Interactions via Quadratic Constraints....Pages 339-355
Semiclassical Methods in Field Theory....Pages 357-366
Quasi-Classical use of Trace Identities in one and Higher Dimensional Field Theories....Pages 367-376
Dynamical Conservation Laws in the Quantized Massive Thirring Model....Pages 377-378
Higher Conservation Laws in the Massive Thirring Model....Pages 379-383
Quantum Field Theory of Kinks in Two-Dimensional Space-Time....Pages 385-417
Probabilistic Approach to Critical Behavior....Pages 419-446
Back Matter....Pages 469-473
On the Equivalence of Different Renormalization Groups....Pages 447-468

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Content:
Front Matter....Pages i-x
A Tutorial Course in Constructive Field Theory....Pages 1-34
Functional Integral Methods in Quantum Field Theory....Pages 35-66
How to Parametrize the Solutions of Lagrangian Field Theories: Symmetry Breaking, and Dimensional Interpolation and Renormalization in the (ϕ4)n Model....Pages 67-77
Phase Transitions in Statistical Mechanics and Quantum Field Theory....Pages 79-130
Continuous Symmetry Breakdown in 2+ε Dimension: The Non-Linear σ Model....Pages 131-142
Quantum Chromodynamics on a Lattice....Pages 143-172
Gauge Theories on the Lattice....Pages 173-199
Continuum Gauge Theories....Pages 201-224
Massless Renormalizable Field Theories and the Yang-Mills Field....Pages 225-239
Conformal Invariant Quantum Field Theory....Pages 241-264
Regularized Quantum Field Theory....Pages 265-279
On Non-Renormalizable Interactions....Pages 281-305
The Classical Sine Gordon Theory....Pages 307-338
Interactions via Quadratic Constraints....Pages 339-355
Semiclassical Methods in Field Theory....Pages 357-366
Quasi-Classical use of Trace Identities in one and Higher Dimensional Field Theories....Pages 367-376
Dynamical Conservation Laws in the Quantized Massive Thirring Model....Pages 377-378
Higher Conservation Laws in the Massive Thirring Model....Pages 379-383
Quantum Field Theory of Kinks in Two-Dimensional Space-Time....Pages 385-417
Probabilistic Approach to Critical Behavior....Pages 419-446
Back Matter....Pages 469-473
On the Equivalence of Different Renormalization Groups....Pages 447-468
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