Related papers: Pulling the straps of polygons
In the present article we describe a class of algebraic curves on which rational functions of two arguments may reach all their possible limiting values. We also solve a similar question for functions that can be represented as a uniform…
In this article we use the Desargues' theorem and its reciprocal to solve two problems.
Wilson loop expectation in 4D $\mathbb{Z}_2$ lattice gauge theory is computed to leading order in the weak coupling regime. This is the first example of a rigorous theoretical calculation of Wilson loop expectation in the weak coupling…
We study the divergences of Wilson loops for a contour with a cusp of zero opening angle, combined with a nonzero discontinuity of its curvature. The analysis is performed in lowest order, both for weak and strong coupling. Such a spike…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
In planar maximally supersymmetric Yang-Mills, we can compute three-point functions at weak coupling using the so-called hexagonalization formalism. The main objects in this framework are called hexagons. We are interested in two sectors of…
We present a new method to compute short-time expectation values in large collective spin systems with generic Markovian decoherence. Our method is based on a Taylor expansion of a formal solution to the equations of motion for Heisenberg…
In this paper, we enumerate Newton polygons asymptotically. The number of Newton polygons is computable by a simple recurrence equation, but unexpectedly the asymptotic formula of its logarithm contains growing oscillatory terms. As the…
The standard prescription for computing Wilson loops in the AdS/CFT correspondence in the large coupling regime and tree-level involves minimizing the string action. In many cases the action has more than one saddle point as in the simple…
We investigate the high energy behavior of the correlation functions of the open Wilson lines in noncommutative gauge theory. We obtain a very simple physical picture that they are bound to form a group of closed Wilson loops. We prove our…
This Ph.D. thesis reaches two main results. The first one is represented by a detailed study, in Feynman gauge, of the perturbative ${\cal O}(g^4)$ contribution to a space-time Wilson loop, with respect to its (expected) Abelian-like time…
We outline two methods of constructing improved composite operators using Wilson fermions.
We begin with an improvement to an extension result for subharmonic functions of Blanchet et al. With the aid of this improvement we then give extension results for subharmonic functions, for separately subharmonic functions, for harmonic…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.
We prove a realization theorem for rational functions of several complex variables which extends the main theorem of M. Bessmertnyi, "On realizations of rational matrix functions of several complex variables," in Vol. 134 of Oper. Theory…
The primary goal of this paper is to study topological invariants in two dimensional twofold rotation and time-reversal symmetric spinful systems. In this paper, firstly we build a new homotopy invariant based on the lifting of the Wilson…
We calculate the change of the properties of a resonator, when coupled to a semiclassical spin by means of the magnetic field. Starting with the Lagrangian of the complete system, we provide an analytical expression for the linear response…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
A systematic loop expansion is formulated in terms of full propagators and vertices. It is based on an expansion of the general solution of an exact non-perturbative flow equation.