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


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 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 in quatum mechanics, but provide only an introduction to the arising in field theory, classical mechanics, and partial equations.

Finally, some of the material developed in this volume will not find 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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    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

    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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