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An explicit quantization is given of certain skew-symmetric solutions of the classical Yang-Baxter, yielding a family of $R$-matrices which generalize to higher dimensions the Jordanian $R$-matrices. Three different approaches to their…
We study a functional that derives from the classical Yang-Mills functional and Born-Infeld theory. We establish its first variation formula and prove the existence of critical points. We also obtain the second variation formula.
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…
The solution of the classical field equation generates the sum of all tree graphs. We show that the classical equation reduces to an easily solved ordinary differential equation for certain multiparticle threshold amplitudes and compute…
We discuss a method for computing the generating function for the multiplicity distribution in field theories with strong time dependent external sources. At leading order, the computation of the generating function reduces to finding a…
I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills…
We provide a concise approach to generalized dilaton theories with and without torsion and coupling to Yang-Mills fields. Transformations on the space of fields are used to trivialize the field equations locally. In this way their solution…
The solutions of two-dimensional gravity following from a non-linear Lagrangian L = f(R) are classified, and their symmetry and singularity properties are described. Then a conformal transformation is applied to rewrite these solutions as…
We demonstrate that the tree level amplitudes and the explicit formulas of soft factors can be uniquely determined by soft theorems and the universality of soft factors. By imposing the soft theorems and the universality, as well as the…
We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected)…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
The Exponential Formula allows one to enumerate any class of combinatorial objects built by choosing a set of connected components and placing a structure on each connected component which depends only on its size. There are multiple…
The gravitational form factors of a hadron are defined through the matrix elements of the energy-momentum tensor current, which can be decomposed into the quark and gluonic parts, between the hadronic states. These form factors provide…
We find wide class of exact solutions of Yang-Mills-Chern-Simons theory coupled to an external source, in terms of doubly periodic Jacobi elliptic functions. The obtained solutions include localized solitons, trigonometric solutions, pure…
Classical dynamical $r$-matrices arise naturally in the combinatorial description of the phase space of Chern-Simons theories, either through the inclusion of dynamical sources or through a gauge-fixing procedure involving two punctures.…
New formulas for the construction of Pythagorean triples and generalizations to equations of higher powers. Application of formulas to some problems, in particular Fermat's equation with n=4.
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. Applying our methods to several field theories such as abelian BF, Chern-Simons and 2-dimensional…
Sometime ago it was shown that the operatorial approach to classical mechanics, pioneered in the 30's by Koopman and von Neumann, can have a functional version. In this talk we will extend this functional approach to the case of classical…