Related papers: Operator product expansion and non-perturbative re…
The two-dimensional O(3) nonlinear sigma model is a well known toy model for studying non-perturbative phenomena in quantum field theory. A central challenge is the renormalization of the energy-momentum tensor, which is complicated by the…
The paper presents a model-independent, nonperturbative proof of operator product expansions in quantum field theory. As an input, a recently proposed phase space condition is used that allows a precise description of point field…
The operator product expansion is used to compute the matrix elements of composite renormalized operators on the lattice. We study the product of two fundamental fields in the two-dimensional sigma-model and discuss the possible sources of…
We obtain the operator product expansion of the self-energy in the O(N) non-linear $\sigma$-model to all orders in the coupling and the large momentum, and to next-to-leading order in 1/N. In the light of this result we discuss recent…
We propose an operator product expansion for planar form factors of local operators in $\mathcal{N}=4$ SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their…
Non-perturbative renormalization of lattice composite operators plays a crucial role in many applications of lattice field theory. We sketch the general problems involved in this task and the methods which are currently used to cope with…
We study the renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative complex scalar field theory. The proper operator basis is defined and it is proved that the bare composite operators are…
We consider the one-loop renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative \phi^4 scalar field theory. Proper operator bases are constructed and it is proved that the bare composite…
In this paper, we propose a complex approach to evaluate a function sum of two noncommuting non Hermitian operators. Then, it is proposed an explicit expansion of the evolution operator in the case of the neutral K-meson system under the…
We study how to compute the operator product expansion coefficients in the exact renormalization group formalism. After discussing possible strategies, we consider some examples explicitly, within the $\epsilon$-expansions, for the…
In logarithmic conformal field theory, primary fields come together with logarithmic partner fields on which the stress-energy tensor acts non-diagonally. Exploiting this fact and global conformal invariance of two- and three-point…
The long-term goal of this project is the non-perturbative renormalization of the energy-momentum tensor in the 2d $O(3)$ non-linear sigma model using different methods which have been developed for QCD applications. As a first step, we…
We compute non-perturbatively the evolution of the twist-2 operators corresponding to the average momentum of non-singlet quark densities. The calculation is based on a finite-size technique, using the Schr\"odinger Functional, in quenched…
We present our progresses in the use of the non-perturbative renormalization framework based on considering QCD at finite temperature with shifted and twisted (for quarks only) boundary conditions in the compact direction. We report our…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
We apply a recently introduced non-perturbative renormalization method to two types of lattice operators: the $\Delta S=2$ four fermion operator and the heavy-light static axial current, which are relevant for the physics of $K$ and $B$…
We propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from…
Motivated by the mixing of UV and IR effects, we test the OPE formula in noncommutative field theory. First we look at the renormalization of local composite operators, identifying some of their characteristic IR/UV singularities. Then we…
We study perturbative renormalization of the composite operators in the $T\bar T$-deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases.…