Full Description
Nowadays it is becoming clearer and clearer that, in the description of natural phenomena, the triadic scheme - microseopie, mesoscopic, macroscopic - is only a rough approximation and that there are many levels of description, probably an infinite hierarchy, in which the specific properties of a given level express some kind of cumulative or collective behaviour of properties or sys tems corresponding to the lower levels. One of the most interesting challenges for contemporary natural sciences is the comprehension of the connections among these different levels of description of reality and the deduction of the laws of higher levels in this hierarchy from basic laws corresponding to lower levels. Since these cumulative or collective phenomena are, typically, nonlin ear effects, the transition from this general program to concrete scientific achievements requires the developement of techniques which allow physical information to be extracted from nonlinear quantum systems. Explicitly in tegrable examples of such systems are rare, and the most interesting physical phenomena are not captured by them. Even in the case of linear systems the fact that an explicit solution is formally available is often useless, since it is impossible to interpret interesting physical phenomena from it.
Contents
1. Notations and Statement of the Problem.- 2. Quantum Fields.- 3. Those Kinds of Fields We Call Noises.- 4. Open Systems.- 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.- 12. Particles Interacting with a Boson Field.- 13. The Anderson Model.- 14. Field—Field Interactions.- 15. Analytical Theory of Feynman Diagrams.- 16. Term-by-Term Convergence.- References.
