Methods of Modern Mathematical Physics Vol. 2 – Michael Reed, Barry Simon – 1st Edition

Description

This volume will serve several purposes: to provide an introduction for graduate not previously acquainted with the material, to serve as a 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 , but provide only an introduction to the arising in 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.

Table of Content


X: THE FOURIER TRANSFORM
1. The Fourier transform on 9°(R") and 9”(R"), convolutions
2. The range of the Fourier transform: Classical spaces
3. The range of the Fourier transform: Analyticity
4. Lp Estimates
Appendix Abstract interpolation
5. Fundamental solutions of partial differential equations with constant coefficients
6. Elliptic regularity
7. The free Hamiltonian for nonrelativistic quantum mechanics
8. The Garding-Wightman axioms
Appendix Lorentz invariant measures
9. Restriction to submanifolds
10. Products of distributions, wave front sets, and oscillatory integrals

X: SELF-ADJOINTNESS AND THE EXISTENCE OF DYNAMICS
1. Extensions of symmetric operators
Appendix Motion on a half-line, limit point-limit circle methods
2. Perturbations of self-adjoint operators
3. Positivity and self-adjointness I: Quadratic forms
4. Positivity and self-adjointness II: Pointwise positivity
5. The commutator theorem
6. Analytic vectors
7. Free quantum fields
Appendix The Weyl relations for the free field
8. Semigroups and their generators
9. Hypercontractive semigroups
10. Graph Limits
11. The Feynman-Kac formula
12. Time-dependent H amiltonians
13. Classical nonlinear wave equations
14. The Hilbert space approach to classical mechanics

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