Related papers: The scaling and mass expansion
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence…
In the present paper we extend to the massive case the procedure of divergences subtraction, previously introduced for the massless nonlinear sigma model (D=4). Perturbative expansion in the number of loops is successfully constructed. The…
We establish sharp stability results for of non--selfadjoint the ascent and descent spectra under strong resolvent convergence (SRS), a natural framework for finite element approximations of non-selfadjoint and singularly perturbed…
Turning the divergent epsilon-expansion into a numerically sensible algorithm, relies on the knowledge of the behaviour of the large order contributions. Two different pictures are known to compete there. The first one was based on…
Feynman diagrams are the foremost tool in the perturbative study of quantum field theory. In gauge theories, the full potential of this tool is revealed when it is combined with the Slavanov-Taylor identities associated with the local gauge…
We show that the accelerated expansion of the Universe can be viewed as a crossover phenomenon where the Newton constant and the Cosmological constant are actually scaling operators, dynamically evolving in the attraction basin of a…
Diffusion models have emerged as a powerful framework in generative modeling, typically relying on optimizing neural networks to estimate the score function via forward SDE simulations. In this work, we propose an alternative method that is…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just renormalizable theory, and allows the…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
The renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by the Gaussian self-similar velocity field with finite, and not small, correlation time. The inertial-range energy…
Free massless scalars have a shift symmetry. This is usually broken by gauge and Yukawa interactions, such that quantum corrections induce a quadratically divergent mass term. In the Standard Model this leads to the hierarchy problem of the…
We introduce a hierarchical system of approximations for summing both conventional perturbation theory and large N vector expansions of models in quantum field theory and condensed matter physics. Each stage of the hierarchy consists of a…
We discuss the feasibility of applying Diagrammatic Monte-Carlo algorithms to the weak-coupling expansions of asymptotically free quantum field theories, taking the large-$N$ limit of the $O(N)$ sigma-model as the simplest example where…
Standard field theoretic renormalization group is applied to the model of landscape erosion introduced by R. Pastor-Satorras and D. H. Rothman [Phys. Rev. Lett. 80: 4349 (1998); J. Stat. Phys. 93: 477 (1998)] yielding unexpected results:…
The asymptotic behavior of the effective mass $m_{\rm eff}(\Lambda)$ of the so-called Nelson model in quantum field theory is considered, where $\Lambda$ is an ultraviolet cutoff parameter of the model. Let $m$ be the bare mass of the…
For $d \ge 2$, let $X$ be a random vector having a Bingham distribution on $\mathcal{S}^{d-1}$, the unit sphere centered at the origin in $\R^d$, and let $\Sigma$ denote the symmetric matrix parameter of the distribution. Let $\Psi(\Sigma)$…
Correlation functions of matrix-valued fields are not generally known for massive renormalized field theories. We find the large-N limit of form factors of the (1+1)-dimensional sigma model with SU(N) X SU(N) symmetry. These form factors…