3 research outputs found
PT Invariant Complex E (8) Root Spaces
We provide a construction procedure for complex root spaces invariant under antilinear transformations, which may be applied to any Coxeter group. The procedure is based on the factorisation of a chosen element of the Coxeter group into two factors. Each of the factors constitutes an involution and may therefore be deformed in an antilinear fashion. Having the importance of the E(8)-Coxeter group in mind, such as underlying a particular perturbation of the Ising model and the fact that for it no solution could be found previously, we exemplify the procedure for this particular case. As a concrete application of this construction we propose new generalisations of Calogero-Moser Sutherland models and affine Toda field theories based on the invariant complex root spaces and deformed complex simple roots, respectively
The Bullough-Dodd model coupled to matter fields
The Bullough-Dodd model is an important two dimensional integrable field
theory which finds applications in physics and geometry. We consider a
conformally invariant extension of it, and study its integrability properties
using a zero curvature condition based on the twisted Kac-Moody algebra
A_2^{(2)}. The one and two-soliton solutions as well as the breathers are
constructed explicitly . We also consider integrable extensions of the
Bullough-Dodd model by the introduction of spinor (matter) fields. The
resulting theories are conformally invariant and present local internal
symmetries. All the one-soliton solutions, for two examples of those models,
are constructed using an hybrid of the dressing and Hirota methods. One model
is of particular interest because it presents a confinement mechanism for a
given conserved charge inside the solitons.Comment: 48 pages, 3 eps figures, late
Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation
A class of non-Dirac-hermitian many-particle quantum systems admitting
entirely real spectra and unitary time-evolution is presented. These quantum
models are isospectral with Dirac-hermitian systems and are exactly solvable.
The general method involves a realization of the basic canonical commutation
relations defining the quantum system in terms of operators those are hermitian
with respect to a pre-determined positive definite metric in the Hilbert space.
Appropriate combinations of these operators result in a large number of
pseudo-hermitian quantum systems admitting entirely real spectra and unitary
time evolution. Examples of a pseudo-hermitian rational Calogero model and XXZ
spin-chain are considered.Comment: To appear in the Special Issue PHHQP 2010, International Journal of
Theoretical Physics; 16 pages, LateX, no figur