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J. Sanchez-Guillen

Publications and source records attributed to J. Sanchez-Guillen.

64 records · Page 4Linked to original sources
arXiv2005

Integrability from an abelian subgroup of the diffeomorphism group

It has been known for some time that for a large class of non-linear field theories in Minkowski space with two-dimensional target space the complex eikonal equation defines integrable submodels with infinitely many conservation laws. These conservation laws are related to the area-preserving diffeomorphisms on target space. Here we demonstrate that for all these theories there exists, in fact, a weaker integrability condition which again defines submodels with infinitely many conservation laws. These conservation laws will be related to an abelian subgroup of the group of area-preserving diffeomorphisms. As this weaker integrability condition is much easier to fulfil, it should be useful in the study of those non-linear field theories.

hep-th↗
arXiv2005

Knot soliton models, submodels, and their symmetries

For some non-linear field theories which allow for soliton solutions, submodels with infinitely many conservation laws can be defined. Here we investigate the symmetries of the submodels, where in some cases we find a symmetry enhancement for the submodels, whereas in others we do not.

hep-th↗
arXiv2005

New tests and applications of the worldline path integral in the first order formalism

We present different non-perturbative calculations within the context of Migdal's representation for the propagator and effective action of quantum particles. We first calculate the exact propagators and effective actions for Dirac, scalar and Proca fields in the presence of constant electromagnetic fields, for an even-dimensional spacetime. Then we derive the propagator for a charged scalar field in a spacelike vortex (i.e., instanton) background, in a long-distance expansion, and the exact propagator for a massless Dirac field in 1+1 dimensions in an arbitrary background. Finally, we present an interpretation of the chiral anomaly in the present context, finding a condition that the paths must fulfil in order to have a non-vanishing anomaly.

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arXiv2005

Generalized integrability conditions and target space geometry

In some higher dimensional nonlinear field theories integrable subsectors with infinitely many conservation laws have been identified by imposing additional integrability conditions. Originally, the complex eikonal equation was chosen as integrability condition, but recently further generalizations have been proposed. Here we show how these new integrability conditions may be derived from the geometry of the target space and, more precisely, from the Noether currents related to a certain class of target space transformations.

hep-th↗
arXiv2005

The symmetries of the Dirac--Pauli equation in two and three dimensions

We calculate all symmetries of the Dirac-Pauli equation in two-dimensional and three-dimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. We construct explicitly a class of multiple zero modes with their gauge potentials.

hep-th↗
arXiv2004

Symmetries of generalized soliton models and submodels on target space $S^2$

Some physically relevant non-linear models with solitons, which have target space $S^2$, are known to have submodels with infinitly many conservation laws defined by the eikonal equation. Here we calculate all the symmetries of these models and their submodels by the prolongation method. We find that for some models, like the Baby Skyrme model, the submodels have additional symmetries, whereas for others, like the Faddeev--Niemi model, they do not.

hep-th↗
arXiv2004

Tests and applications of Migdal's particle path-integral representation for the Dirac Propagator

We derive some non-perturbative results in 1+1 and 2+1 dimensions within the context of the particle path-integral representation for a Dirac field propagator in the presence of an external field, in a formulation introduced by Migdal in 1986. We consider the specific properties of the path-integral expressions corresponding to the 1+1 and 2+1 dimensional cases, presenting a derivation of the chiral anomaly in the former and of the Chern-Simons current in the latter. We also discuss particle propagation in constant electromagnetic field backgrounds.

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arXiv2000

Infinite symmetries in the Skyrme model

We show that the Skyrme theory possesses a submodel with an infinite number of local conserved currents. The constraints leading to the submodel explore a decomposition of SU(2) with a complex field parametrizing the symmetric space SU(2)/U(1) and a real field in the direction of U(1). We demonstrate that the Skyrmions of topological charges $\pm 1$ belong to such integrable sector of the theory. Our results open ways to the development of exact methods, compensating for the non-existence of a BPS type sector in the Skyrme theory.

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