Map from one-dimensional quantum field theory to quantum chaos on a two-dimensional torus

Chaos in a One-dimensional Integrable Quantum System

We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties are nontrivial. The level spacing distribution between its neighboring odd and even levels displays a surprising agreement with the prediction obtained for the...

Two-dimensional Quantum Field Theory, examples and applications

The main principles of two-dimensional quantum field theories, in particular two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects of these theories which make them particularly valuable for testing ideas of four-dimensional quantum field theory. The dynamics of confinement and theta vacuum are explained by using the non-perturbative methods developed in two dimensions...

Braid group statistics in two-dimensional quantum field theory

Within the framework of algebraic quantum field theory, we construct explicitly localized morphisms of a Haag-Kastler net in 1 + 1dimensional Minkowski space showing abelian braid group statistics. Moreover, we investigate the scattering theory of the corresponding quantum fields.

Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory

Path Integration in Two-dimensional Topological Quantum Field Theory

A positive, di eomorphism-invariant generalized measure on the space of metrics of a two-dimensional smooth manifold is constructed. We use the term generalized measure analogously with the generalized measures of Ashtekar and Lewandowski and of Baez. A family of actions is presented which, when integrated against this measure give the two-dimensional axiomatic topological quantum eld theories,...