Introduction to simple integrable models of quantum field theory

Pasquale Calabrese, Fabian H. L. Eßler, Giuseppe Mussardo

Introduction to the field of quantum integrable models

Tai Kai Ng

PART I 1. Introduction 2. Lagrangian Formulation of Classical Mechanics and Field Theory 3. Quantization of Classical Field Theory I 4. Quantization of Classical Field Theory II 5. Berry Phase and Gauge Theory 6. Introduction to Perturbation Theory PART II 7. Concept of Effective Field Theory, Phases, and Phase Transition 8. Non-Linear Effects and Topology in Quantum Field Theory 9. Simple Bose Liquids - Introduction to Superfluidity 10. Simple Fermi Liquids - Introduction to Fermi Liquid Theory 11. Introduction to BCS Theory (S-Wave Superconductors) 12. Introduction to Quantum Magnetism

武夫 稲見, 隆 佐々木

Gesualdo Delfino A, Giuseppe Mussardo, P. Simonetti

Marcio Jose Martins

The author discusses the ground state and some elementary excitations of the B p non-simple laced integrable models. The zeros of the associated Bethe ansatz equations are characterized by a special distribution in the complex plane, which is different from the usual string hypothesis. The introduction of this new solution makes it possible to calculate exactly various properties in the thermodynamic limit. The finite-size corrections to the eigenspectrum strongly suggest that the B p Wess-Zumino-Witten-Novikov models are the underlying conformal field theory for these non-simple laced models.

Stijn Jurrien van Tongeren

Abstract We give a pedagogical introduction to the thermodynamic Bethe ansatz, a method that allows us to describe the thermodynamics of integrable models whose spectrum is found via the (asymptotic) Bethe ansatz. We set the stage by deriving the Fermi–Dirac distribution and associated free energy of free electrons, and then in a similar though technically more complicated fashion treat the thermodynamics of integrable models, focusing first on the one-dimensional Bose gas with delta function interaction as a clean pedagogical example, secondly the XXX spin chain as an elementary (lattice) model with prototypical complicating features in the form of bound states, and finally the SU ( 2 ) chiral Gross–Neveu model as a field theory example. Throughout this discussion we emphasize the central role of particle and hole densities, whose relations determine the model under consideration. We then discuss tricks that allow us to use the same methods to describe the exact spectra of integrable field theories on a circle, in particular the chiral Gross–Neveu model. We moreover discuss the simplification of TBA equations to Y systems, including the transition back to integral equations given sufficient analyticity data, in simple examples.