arXiv subjects

Joaquin Sanchez Guillen

Publications and source records attributed to Joaquin Sanchez Guillen.

3 recordsLinked to original sources

arXiv1997

Aspects of Solitons in Affine Integrable Hierarchies

We argue that one of the basic ingredients for the appearance of soliton solutions in integrable hierarchies, is the existence of ``vacuum solutions'' corresponding to Lax operators lying in some abelian subalgebra of the associated affine Kac-Moody algebra. Using the dressing transformation we construct the solutions in the orbit of those vacuum solutions, and conjecture that the solitons correspond to some special points in those orbits. The generalized tau-function for those hierarchies are defined for integrable highest weight representations. It applies for any level of the representation. We illustrate our methods with the recently proposed non abelian Toda models coupled to matter fields. A very special class of such theories possess a U(1) Noether charge that is proportional to a topological charge. That leads to a mechanism that confines the matter fields inside the solitons.

solv-int↗

arXiv1991

Universality and Non-Perturbative Definitions of 2D Quantum Gravity from Matrix Models

The universality of the non-perturbative definition of Hermitian one-matrix models following the quantum, stochastic, or $d=1$-like stabilization is discussed in comparison with other procedures. We also present another alternative definition, which illustrates the need of new physical input for $d=0$ matrix models to make contact with 2D quantum gravity at the non-perturbative level.

hep-th↗

arXiv1991

Instantons in the Quantum Framework of 2D Gravity

We analyze the non--perturbative features of 2D quantum gravity defined by stochastic regularization of the unstable matrix model showing, first, that the WKB approximation of the well-defined quantum Fokker-Planck hamiltonian corresponds to the semiclassical eigenvalue density of the former. The double scaled potential exhibits an instanton--like behaviour, which is universal and scales, but whose interpretation in terms of pure gravity is still open.

hep-th↗