Research Catalog

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

Title
Linear infinite particle operators / V.A. Malyshev, R.A. Minlos.
Author
Malyshev, V. A. (Vadim Aleksandrovich)
Publication
Providence, RI : American Mathematical Society, 1995.

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TextRequest in advance QC20.7.O65 M35 1995Off-site

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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