Quantum field theory, bosonization and duality on the half line

Abstract

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.

Integrating geometry in general 2D dilaton gravity with matter

“…As expected, the solution of eqs. (39-41) coincides with the quantities B (0) i = B i (j = 0) as defined in (25,26) and (30) for j i = 0 and S = 0:…”

“…We first treat approach a). ForB 1 andB 2 the terms O(S 2 ) can be read off from (25,26). ForB 3 they can be summarized in the nonlocal expression H xy asB…”

Quantum Group Symmetry of Integrable Systems With or Without Boundary

“…We remind here the results obtained by Mintchev et al [6,7], following [4,5], on the quantum integrable systems with boundary. As for the case without boundary, the central role is played by an algebra which both encodes the asymptotic states of the system and the effect of the boundary.…”

Junctions of anyonic Luttinger wires

“…For all these reasons, we investigate in this paper the Tomonaga-Luttinger (TL) model on a junction with an arbitrary number n of arms as depicted in Fig. 1 (a junction with two wires n = 2 can be seen as a defect on the line, a problem that has been largely investigated [29][30][31][32][33][34][35][36][37][38][39][40] in the past). To solve this problem, at the junction we impose conditions that are probably not obvious for an electronic problem, but they show the advantage to be exactly solvable.…”