Chaiho Rim

Integrable quantum field theory with boundaries: the exact g-function

The g-function was introduced by Affleck and Ludwig in the context of critical quantum systems with boundaries. In the framework of the thermodynamic Bethe ansatz (TBA) method for relativistic scattering theories, all attempts to write an exact integral equation for the off-critical version of this quantity have, up to now, been unsuccessful. We tackle this problem by using an n-particle cluster expansion, close in spirit to form-factor calculations of correlators on the plane. The leading contribution already disagrees with all previous proposals, but a study of this and subsequent terms allows us to deduce an exact infrared expansion for g, written purely in terms of TBA pseudoenergies. Although we only treat the thermally-perturbed Ising and the scaling Lee–Yang models in detail, we propose a general formula for g which should be valid for any model with entirely diagonal scattering.

Reflection factors and exact g-functions for purely elastic scattering theories

We discuss reflection factors for purely elastic scattering theories and relate them to perturbations of specific conformal boundary conditions, using recent results on exact off-critical g-functions. For the non-unitary cases, we support our conjectures using a relationship with quantum group reductions of the sine-Gordon model. Our results imply the existence of a variety of new flows between conformal boundary conditions, some of them driven by boundary-changing operators.

Background Fermi Fields and Schwinger-dewitt Proper Time Method

Abstract By using supermatrices and the super-Fredholm determinant, the Schwinger-DeWitt propertime expansion method is generalized to the case with background Fermi fields as well as background Bose fields. For quantum field theories defined in flat or curved space-time, we present a derivation of complete one-loop renormalization counterterms (including those involving Fermi fields) by this method. The whole one-loop counterterms are given in terms of the supertrace of a single coefficient a2 - a supermatrix - appearing in the DeWitt-WKB expansion.

Exact g-function flow between conformal field theories

Abstract Exact equations are proposed to describe g -function flows in integrable boundary quantum field theories which interpolate between different conformal field theories in their ultraviolet and infrared limits, extending previous work where purely massive flows were treated. The approach is illustrated with flows between the tricritical and critical Ising models, but the method is not restricted to these cases and should be of use in unravelling general patterns of integrable boundary flows between pairs of conformal field theories.

Abelian Chern-Simons field theory and the anyon equation on a torus.

We quantize the Abelian Chern-Simons theory coupled to a nonrelativistic matter field on a torus without invoking the flux quantization. Through a series of canonical transformations which is equivalent to solving the Gauss constraint, we obtain an effective Hamiltonian density with a periodic matter field. We also obtain the many-anyon Schroedinger equation with periodic Aharonov-Bohm potentials and analyze the periodic property of the wave function. Some comments are given on the different features of our approach from the previous ones.

EXACT WAVE FUNCTIONS OF MULTI-SPECIES ANYON QUANTUM MECHANICS

We investigate the many-anyon quantum-mechanical system of multi-species and obtain algebraically the energy and the angular momentum eigenstates in a harmonic potential well, in a constant magnetic field and of free system using ladder operators. The eigenvalues and their multiplicity of the eigenstates are given.

ABELIAN CHERN–SIMONS THEORY WITH MATTER FIELDS

It is shown that in the Abelian Chern–Simons plus Maxwell theory in 1 + 2 dimensions there is a unitary transformation such that massless modes of the gauge field are eliminated completely in the Hilbert space and a nonlocal interaction between matter fields (fermions or scalars) remains instead. The nonlocal interaction is given in terms of an effective gauge field satisfying the Gauss constraint. It is also pointed out that it is the nonlocal interaction that changes the statistics of pointlike particles and that makes a vortex charged.