The main subject of this book can be viewed in various ways. From the standpoint of functional analysis, it studies spectral properties of a certain class of linear operators; from the viewpoint of probability theory, it is concerned with the analysis of singular Markov processes; and, from the vantage point of mathematical physics, it analyzes the dynamics of equilibrium systems in quantum statistical physics and quantum field theory. Malyshev and Minlos describe two new approaches to the subject which have not been previously treated in monograph form. They also present background material which makes the book accessible and useful to researchers and graduate students working in functional analysis, probability theory, and mathematical physics.

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zlib/Mathematics/V. A. Malyshev and R. A. Minlos/Linear Infinite-Particle Operators_2693519.djvu

Linear infinite particle operators

Vadim Aleksandrovich Malyshev; Robert Adolʹfovich Minlos

V. A. Malyshev, R. A. Minlos; [Transl. by Alan Mason]

V A Malyshev, (Vadim Aleksandrovich)

Vadim Aleksandrovič̌ Malyšev

Малышев, Вадим Александрович

Education Development Center, Incorporated

Translations of mathematical monographs ;, v. 143, Providence, RI, Rhode Island, 1995

Translations of mathematical monographs, Providence, RI, cop. 1995

American Mathematical Society, [N.p.], 2018

United States, United States of America

Providence (R. I.), Unknown, 1995

0

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Includes bibliographical references (p. 295-298).

Библиогр.: с. 295-298

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Introduction. What This Book Is About -- Ch. 0. Extended Introduction -- 2. Basic Examples Of Physical Systems -- 3. Infinite Systems And The Thermodynamic Limit -- 4. Expansion Of Heisenberg Dynamics -- 5. Euclidean Approach -- 6. Corpuscular Picture (quasiparticles And Scattering Theory For Infinite Quantum Systems) -- Ch. 1. Construction Of A Nonequilibrium Dynamics -- 1. The Dynamics Of An Infinite One-dimensional Classical Gas Of Interacting Solid Rods -- 2. A Quick Review Of C*-algebras -- 3. Fock Spaces And Second-quantization Operators -- 4. The Car Algebra And Its Free Dynamics. Dynamics Of A System Of Interacting Fermions. Analog Of Robinson's Theorem -- 5. Linear Dynamics For Fermion And Boson Systems -- 6. Random Dynamics (stochastic Langevin Equations) -- 7. Marginally Closed Markov Chains With Local Interaction -- Ch. 2. Construction Of An Equilibrium Dynamics -- 1. Ground And Temperature States -- 2. Ground State For An Infinite System Of Harmonic Oscillators -- 3. A Free Quasistate -- 4. Fock Representation For The Dynamics Of Free Systems -- 5. The Euclidean Approach -- 6. Euclidean Fields For Temperature States. The Modular Operator -- Ch. 3. Spectral Analysis Of The Euclidean Field Transfer Matrix -- 1. Cluster Expansion Of The Transfer Matrix -- 2. Cluster Operators. Definition And Basic Properties -- 3. Invariant K-particle Subspaces Of A Cluster Operator -- 4. Some Examples -- 5. Spectral Analysis Of The Transfer Matrix For A Fermion Field -- 6. Continuous-time Models -- 7. Spectral Analysis Of K-particle Cluster Operators -- 8. Asymptotic Decay Of The Correlation Functions For Gibbs Fields -- Ch. 4. Asymptotic Completeness For Interacting Fermion Systems -- 1. Fermi Systems With Bounded Interaction -- 2. Asymptotic Completeness For Interactions With Vacuum Polarization (linked Cluster Theorem) -- 3. Fermi Gas Interacting Weakly With A Particle -- 4. Weak-interaction Limit For A Quantum Schrodinger Particle Interacting With Fermi Gas -- Ch. 5. The Method Of Bethe-salpeter Kernels (dyson's Equation) -- 1. The Dyson Equation And The Bethe-salpeter Kernel Method For The Ising Field -- 2. One-particle Spectrum Of The Transfer Matrix For A Gibbs Field With Unbounded Spin. Description Of The Model And Results -- 3. Cluster Expansion Of The Covariance Operators -- 4. Dyson's Equation For The Covariance Operators -- 5. Analytic Structure Of The Green Functions -- Guide To The Literature -- References. V.a. Malyshev, R.a. Minlos. Includes Bibliographical References.

From the standpoint of functional analysis, this book studies spectral properties of a certain class of linear operators. It concerns with the analysis of singular Markov processes from the viewpoint of probability theory. It also analyzes the dynamics of equilibrium systems in quantum statistical physics and quantum field theory.

2016-03-20