Related papers: Operator product expansion and non-perturbative re…
We study the phenomenon of composite operator renormalization and mixing in systems where time-translational invariance is broken and the evolution is out-of-equilibrium. We show that composite operators mix also through non-local memory…
We consider the operator product expansion (OPE) of correlation functions in the supersymmetric $O(N)$ non-linear sigma model at sub-leading order in the large $N$ limit in order to study the cancellation between ambiguities coming from…
An arbitrary form of complex potential perturbation in an oscillator consists of many exciting questions in open quantum systems. These often provide valuable insights in a realistic scenario when a quantum system interacts with external…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
In general, perturbative expansions of observables in powers of the coupling constant in quantum field theories are asymptotic series. In many cases it is possible to apply resummation techniques to assign a unique finite value to an…
Using the nonperturbative functional renormalization group (FRG) within the Blaizot-M\'endez-Galain-Wschebor approximation, we compute the operator product expansion (OPE) coefficient $c_{112}$ associated with the operators…
The derivative expansion of the Wilsonian renormalization group generates additional terms in the effective beta-functions not present in the perturbative approach. Applied to the nonlinear sigma model, to lowest order the vanishing of the…
We analyze inclusive $\tau$ decay using a modified version of the $a$ expansion, a non-perturbative technique in which the effective coupling is analytic in the infrared region. The modification involves renormalization group improvement of…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
We review recent studies of the operator product expansion of the plaquette and of the associated determination of the gluon condensate. One first needs the perturbative expansion to orders high enough to reach the asymptotic regime where…
The irreducible tensor operators and their tensor products employing Racah algebra are studied. Transformation procedure of the coordinate system operators act on are introduced. The rotation matrices and their parametrization by the…
We calculate the wave-function renormalization in 2-dimensional O(3) sigma model, non- perturbatively. It is evaluated in a box with a finite spatial extent. We determine the anomalous dimension in the finite volume scheme through an…
Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…
Our aim is to compute the lower moments of the unpolarized and polarized deep-inelastic structure functions of the nucleon on the lattice. The theoretical basis of the calculation is the operator product expansion. To construct operators…
Field theoretical renormalization group methods are applied to the Obukhov--Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $<{\bf v}(t,{\bf x}){\bf v}(t',{\bf x})> - < v(t,{\bf x}){\bf…
A new way to design parameter estimators with enhanced performance is proposed in the paper. The procedure consists of two stages, first, the generation of new regression forms via the application of a dynamic operator to the original…
We study the model of (2 + 1)-dimensional relativistic fermions in a random non-Abelian gauge potential at criticality. The exact solution shows that the operator expansion contains a conserved current - a generator of a continuous…
We present our progress on a study of the $O(3)$ model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct $n$-point correlation functions. We then…
We provide an explicit expression for the renormalized expectation value of the stress-energy tensor of a spin-$1/2$ field in a spatially flat FLRW universe. Its computation is based on the extension of the adiabatic regularization method…
We discuss differential-- versus integral--equation based methods describing out--of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach,…