arXiv subjects

Luiz A. Ferreira

Publications and source records attributed to Luiz A. Ferreira.

7 recordsLinked to original sources

arXiv2026

Quantum Yang-Mills Charges in Strongly Coupled 2D Lattice QCD with Three Flavors

We investigate the quantum properties of the truly gauge-invariant and conserved charges of two-dimensional Yang-Mills theories, focusing on lattice QCD in the strong coupling regime. The construction of those charges uses the integral version of the (1+1)-dimensional Yang-Mills equations, and they correspond to the eigenvalues of a charge operator. The gauge invariance of the charges suggests that they are not confined, hence hadronic states may carry them. Using the path integral formalism with imaginary time (Euclidean), we evaluate the correlation functions of those charges on baryon and meson states through functional integrals over the gauge group SU(N) (N=2,3) and Grassmannian variables - the fermionic fields. Our results show that the expectation values of the lowest non-trivial charges are nonzero for baryon and meson states but vanish for non-gauge-invariant states, supporting the interpretation that hadrons indeed carry these charges. While renormalization effects and higher-order contributions remain to be analyzed, these findings point toward a potential link between gauge-invariant charges and confinement.

hep-lat↗

arXiv2025

$U(1)$ gauged non-topological solitons in the 3+1 dimensional $O(3)$ sigma-model

We present and study new non-topological soliton solutions in the $U(1)$ gauged non-linear $O(3)$ sigma model with a symmetry breaking potential in 3+1 dimensional flat space-time. The configurations are endowed with an electric and magnetic field and also carry a nonvanishing angular momentum density. We discuss properties of these solitons and investigate the domains of their existence.

hep-th↗

arXiv2016

Quasi-integrable deformations of the $SU(3)$ Affine Toda Theory

We consider deformations of the $SU(3)$ Affine Toda theory (AT) and investigate the integrability properties of the deformed theories. We find that for some special deformations all conserved quantities change to being conserved only asymptotically, {\it i.e.} in the process of the scattering of two solitons these charges do vary in time, but they return, after the scattering, to the values they had prior to the scattering. This phenomenon, which we have called quasi-integrability, is related to special properties of the two-soliton solutions under space-time parity transformations. Some properties of the AT solitons are discussed, especially those involving interesting static multi-soliton solutions. We support our analytical studies with detailed numerical ones in which the time evolution has been simulated by the 4th order Runge-Kutta method. We find that for some perturbations the solitons repel and for the others they form a quasi-bound state. When we send solitons towards each other they can repel when they come close together with or without `flipping' the fields of the model. The solitons radiate very little and appear to be stable. These results support the ideas of quasi-integrability, {\it i.e.} that many effects of integrability also approximately hold for the deformed models.

hep-th↗

arXiv1998

Integrable theories in any dimension and homogenous spaces

We construct local zero curvature representations for non-linear sigma models on homogeneous spaces, defined on a space-time of any dimension, following a recently proposed approach to integrable theories in dimensions higher than two. We present some sufficient conditions for the existence of integrable submodels possessing an infinite number of local conservation laws. Examples involving symmetric spaces and group manifolds are given. The $CP^N$ models are discussed in detail.

hep-th↗

arXiv1998

A New Approach to Integrable Theories in any Dimension

The zero curvature representation for two dimensional integrable models is generalized to spacetimes of dimension d+1 by the introduction of a d-form connection. The new generalized zero curvature conditions can be used to represent the equations of motion of some relativistic invariant field theories of physical interest in 2+1 dimensions (BF theories, Chern-Simons, 2+1 gravity and the CP^1 model) and 3+1 dimensions (self-dual Yang-Mills theory and the Bogomolny equations). Our approach leads to new methods of constructing conserved currents and solutions. In a submodel of the 2+1 dimensional CP^1 model, we explicitly construct an infinite number of previously unknown nontrivial conserved currents. For each positive integer spin representation of sl(2) we construct 2j+1 conserved currents leading to 2j+1 Lorentz scalar charges.

hep-th↗

arXiv1997

The structures underlying soliton solutions in integrable hierarchies

We point out that a common feature of integrable hierarchies presenting soliton solutions is the existence of some special ``vacuum solutions'' such that the Lax operators evaluated on them, lie in some abelian subalgebra of the associated Kac-Moody algebra. The soliton solutions are constructed out of those ``vacuum solitons'' by the dressing transformation procedure.

solv-int↗

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↗