Quantum Theory and Its Stochastic Limit

Luigi Accardi, Yun Gang Lu, Igor Volovich

744 pages, parution le 14/08/2002

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Résumé

The subject of this book is a new mathematical technique, the stochastic limit, developed for solving nonlinear problems in quantum theory involving systems with infinitely many degrees of freedom (typically quantum fields or gases in the thermodynamic limit). This technique is condensed into some easily applied rules (called "stochastic golden rules"), which allow us to single out the dominating contributions to the dynamical evolution of systems in regimes involving long times and small effects. In the stochastic limit the original Hamiltonian theory is approximated using a new Hamiltonian theory which is singular. These singular Hamiltonians still define a unitary evolution, and the new equations give much more insight into the relevant physical phenomena than the original Hamiltonian equations. Especially, one can explicitly compute multi-time correlations (e.g. photon statistics) or coherent vectors, which are beyond the reach of typical asymptotic techniques.

Contents

Part I. Statement of the Problem and Simplest Models
1. Notations and Statement of the Problem
2. Quantum Fields
3. Those Kinds of Fields We Call Noises
4 . OpenSystems
5. Spin–Boson Systems
6. Measurements and Filtering Theory
7. Idea of the Proof and Causal Normal Order
8. Chronological Product Approach to the Stochastic Limit
9. Functional Integral Approach to the Stochastic Limit
10. Low-Density Limit: The Basic Idea
11. Six Basic Principles of the Stochastic Limit

Part II. Strongly Nonlinear Regimes
12. Particles Interacting with a Boson Field
13. The Anderson Model
14. Field–Field Interactions

Part III. Estimates and Proofs
15. Analytical Theory of Feynman Diagrams
16. Term-by-Term Convergence

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Luigi Accardi, Yun Gang Lu, Igor Volovich
Parution	14/08/2002
Nb. de pages	744
Format	16 x 24
Couverture	Relié
Poids	853g
Intérieur	Noir et Blanc
EAN13	9783540419280