16 citations · 80 across the 23 of their papers we have counts for
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A monoidal representation for linearized gravity
Ernesto Contreras, Cayetano Di Bartolo, Lorenzo Leal
We propose an alternative representation for linear quantum gravity. It is based on the use of a structure that bears some resemblance to the Abelian loop representation used in el…
Geometric Representation of Interacting Non-Relativistic Open Strings using Extended Objects
P. J. Arias, N. Bolivar, E. Fuenmayor +1
Non-relativistic charged open strings coupled with Abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. The model consists of…
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
Cayetano Di Bartolo, Javier Grau, Lorenzo Leal
A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consiste…
Hamiltonian BF theory and projected Borromean Rings
Ernesto Contreras, Adalberto Díaz, Lorenzo Leal
It is shown that the canonical formulation of the abelian BF theory in D = 3 allows to obtain topological invariants associated to curves and points in the plane. The method consis…
Geometric Representation of the generator of duality in massless and massive form field theories
Ernesto Contreras, Lorenzo Leal, Yisely Martinez
We study the invariance under duality transformations in massless and massive form field theories and obtain the Noether generators of the infinitesimal transformations that co…
Electromagnetism and multiple-valued loop-dependent wave functionals
Lorenzo Leal
We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that t…
The Topological Theory of the Milnor Invariant
Lorenzo Leal, Jesus Pineda
We study a topological Abelian gauge theory that generalizes the Abelian Chern-Simons one, and that leads in a natural way to the Milnor's link invariant when the cl…
Surface-Invariants in 2D Classical Yang-Mills Theory
Rafael Díaz, E. Fuenmayor, Lorenzo Leal
We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as…
Quantization of Interacting Non-Relativistic Open Strings using Extended Objects
P. J. Arias, N. Bolívar, E. Fuenmayor +1
Non-relativistic charged open strings coupled with Abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. The model comprises op…
Loop Equations in Abelian Gauge Theories
Cayetano Di Bartolo, Lorenzo Leal, Francisco Peña
The equations obeyed by the vacuum expectation value of the Wilson loop of Abelian gauge theories are considered from the point of view of the loop-space. An approximative scheme f…
Magnetic Monopole in the Loop Representation
Lorenzo Leal, Alexander Lopez
We quantize the electromagnetic field in the presence of a static magnetic monopole, within the loop-representation formalism. We find that the loop-dependent wave functional becom…
Interacting Particles and Strings in Path and Surface Representations
P. J. Arias, E. Fuenmayor, Lorenzo Leal
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider t…
The space of signed points and the Self Dual Model
Lorenzo Leal
We study a generalization of the group of loops based on sets of signed points, instead of paths or loops. This geometrical setting incorporates the kinematical constraints of the…
A Geometric Approach to Massive p-form Duality
Pio J. Arias, Lorenzo Leal, Jean Carlos Perez-Mosquera
Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators…
Link Invariants from Classical Chern-Simons Theory
Lorenzo Leal
Taking as starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons Theory with non-dynamical sources, we search for analytical expre…
Loop representation of charged particles interacting with Maxwell and Chern-Simons fields
Ernesto Fuenmayor, Lorenzo Leal, Ryan Revoredo
The loop representation formulation of non-relativistic particles coupled with abelian gauge fields is studied. Both Maxwell and Chern-Simons interactions are separately considered…
Maxwell Chern Simons Theory in a Geometric Representation
Lorenzo Leal
We quantize the Maxwell Chern Simons theory in a geometric representation that generalizes the Abelian Loop Representation of Maxwell theory. We find that in the physical sector, t…
Knot Invariants from Classical Field Theories
Lorenzo Leal
We consider the Non-Abelian Chern-Simons term coupled to external particles, in a gauge and diffeomorphism invariant form. The classical equations of motion are perturbativelly stu…
A Geometric Representation for the Proca Model
Jaime Camacaro, Rolando Gaitán, Lorenzo Leal
The Proca model is quantized in an open-path dependent representation that generalizes the Loop Representation of gauge theories. The starting point is a gauge invariant Lagrangian…
Electric-Magnetic duality and the "Loop Representation" in Abelian Gauge Theories
Lorenzo Leal
Abelian Gauge Theories are quantized in a geometric representation that generalizes the Loop Representation and treates electric and magnetic operators on the same footing. The usu…