Methods of Modern Mathematical Physics: Fourier analysis, self-adjointness, Volume 2

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Elsevier, 1975 - Science - 361 pages
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This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III. For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter.
 

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Contents

The Garding Wightman axioms
61
Products of distributions wave front sets and oscillatory
87
Von Neumann Algebras XIX Applications to Quantum Field Theory
114
SELFADJOINTNESS AND THE EXISTENCE OF DYNAMICS Extensions of symmetric operators
135
Applications to Statistical Mechanics
139
Appendix Motion on a halfline limit pointlimit circle methods
146
Perturbations of selfadjoint operators
162
Quadratic forms
176
Semigroups and their generators
235
Hypercontractive semigroups
258
Graph Limits
268
The FeynmanKac formula
274
Timedependent Hamiltonians
282
Classical nonlinear wave equations
293
The Hilbert space approach to classical mechanics
313
Notes
318

Pointwise positivity
182
The commutator theorem
191
Analytic vectors
200
Free quantum fields
207
Appendix The Weyl relations for the free field
231
Problems
338
Reader s Guide
349
List of Symbols
353
Index
355
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