Research Catalog

Title

Linear infinite particle operators / V.A. Malyshev, R.A. Minlos.

Author

Malyshev, V. A. (Vadim Aleksandrovich)

Publication

Providence, RI : American Mathematical Society, 1995.

Items in the Library & Off-site

Holdings

Details

Additional Authors

Minlos, R. A. (Robert Adolʹfovich)

Description

viii, 298 p.; 26 cm.

Series Statement

Translations of mathematical monographs ; v. 143

Uniform Title

• Lineĭnye operatory v beskonechnochastichnykh sistemakh. English
• Translations of mathematical monographs v. 143.

Alternative Title

Lineĭnye operatory v beskonechnochastichnykh sistemakh.

Subject

• Linear operators
• Functional analysis
• Markov processes
• Statistical physics
• Quantum field theory
• Mathematical physics
• Markov Chains

Bibliography (note)

• Includes bibliographical references.

Processing Action (note)

• committed to retain

Contents

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.

ISBN

0821802836

LCCN

^^^94042578^

OCLC

31434380

Owning Institutions

Harvard Library