Some algebraic aspects of field quantization in space-time with boundaries are discussed. We introduce an associative algebra B R , whose exchange properties are inferred from the scattering processes in integrable models with reflecting boundary conditions on the half line. The basic properties of B R are established and the Fock representations associated with certain involutions in B R are derived. We apply these results for the construction of quantum fields and for the study of scattering on the half line.

An operator formalism for bosonization at finite temperature and density is developed. We treat the general case of anyon statistics. The exact n-point correlation functions, satisfying the Kubo-Martin-Schwinger condition, are explicitly constructed. The invariance under both vector and chiral transformations allows to introduce two chemical potentials. Investigating the exact momentum distribution, we discover anyon condensation in certain range of the statistical parameter. Another interesting feature is the occurrence of a non-vanishing persistent current. As an application of the general formalism, we solve the massless Thirring model at finite temperature, deriving the charge density and the persistent current.

We develop a rigorous framework for constructing Fock representations of quantum fields obeying generalized statistics associated with certain solutions of the spectral quantum Yang-Baxter equation. The main features of these representations are investigated. Various aspects of the underlying mathematical structure are illustrated by means of explicit examples.

We develop a bosonization procedure on the half line. Different boundary conditions, formulated in terms of the vector and axial fermion currents, are implemented by using in general the mixed boundary condition on the bosonic field. The interplay between symmetries and boundary conditions is investigated in this context, with a particular emphasis on duality. As an application, we explicitly construct operator solutions of the massless Thirring model on the half line, respecting different boundary conditions.

Articles you may be interested inThe inverse scattering transform for the focusing nonlinear Schrödinger equation with asymmetric boundary conditions J. Math. Phys. 55, 101505 (2014); 10.1063/1.4898768 Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditionsThe nonlinear Schrödinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is constructed. The construction is based on a new algebraic structure, which is called in what follows boundary algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov-Faddeev algebra. The fundamental quantum field theory properties of the solution are established and discussed in detail. The relative scattering operator is derived in the Haag-Ruelle framework, suitably generalized to the case of broken translation invariance in space.