Exactly Solvable Models in Many-Body Theory

The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.

The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.

Contents:

• Low-Order Density Matrices
• Solvable Models for Small Clusters of Fermions
• Small Clusters of Bosons
• Anyon Statistics with Models
• Superconductivity and Superfluidity
• Exact Results for an Isolated Impurity in a Solid
• Pair Potential and Many-Body Force Models for Liquids
• Anderson Localization in Disordered Systems
• Statistical Field Theory: Especially Models of Critical Exponents
• Relativistic Fields
• Towards Quantum Gravity
• Appendices

Readership: Graduate students and researchers in condensed matter theory.