相关论文: Gaussian, Mean Field and Variational Approximation…

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…

We derive universal formulae for integrating out heavy degrees of freedom in scalar field theories up to one-loop level in terms of covariant quantities associated with the geometry of the field manifold. The universal matching results can…

The exploration of scalar field theories that exhibit Carroll and Galilei symmetries has attracted a lot of attention. In this paper, we generalize these studies to fermionic field theories and construct consistent electric and magnetic…

We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…

We propose a mean-field method to calculate approximately the spacing distribution functions $p^{(n)}(s)$ in 1D classical many-particle systems. We compare our method with two other commonly used methods, the independent interval…

We study the domain of validity of a Schwinger-Dyson (SD) approach to non-equilibrium dynamics when there is broken symmetry. We perform exact numerical simulations of the one- and two-point functions of lambda phi^4 field theory in 1+1…

Recently, self-dualities based on saddle-point expansions have been proposed as a means to obtain qualitative non-perturbative information in scalar field theories. In this work, we test this proposition quantitatively by studying the phase…

Using a one-loop approximation for the effective potential in the Higgs model of electrodynamics for a charged scalar field, we argue for the existence of a triple point for the renormalized (running) values of the selfinteraction $\lambda$…

We study the conformal bootstrap constraints for 3D conformal field theories with a $\mathbb{Z}_2$ or parity symmetry, assuming a single relevant scalar operator $\epsilon$ that is invariant under the symmetry. When there is additionally a…

We consider the appearance of multiple scalar fields in SFT inspired non-local models with a single scalar field at late times. In this regime all the scalar fields are free. This system minimally coupled to gravity can be analyzed…

We develop techniques for determining the exact asymptotic speed of convergence in the multidimensional normal approximation of smooth functions of Gaussian fields. As a by-product, our findings yield exact limits and often give rise to…

Bayesian inference has many advantages for complex models, but standard Monte Carlo methods for summarizing the posterior can be computationally demanding, and it is attractive to consider optimization-based variational methods. Our work…

In this paper we consider the Euclidean Steiner tree problem and, more generally, (single sink) Gilbert--Steiner problems as prototypical examples of variational problems involving 1-dimensional connected sets in $\mathbb{R}^n$. Following…

Based on local gauge invariance, four different kinds of fundamental interactions in Nature are unified in a theory which has $SU(3)_c \otimes SU(2)_L \otimes U(1) \otimes_s Gravitational Gauge Group$ gauge symmetry. In this approach,…

We develop an approximation scheme for our worldsheet model of the sum of planar diagrams based on mean field theory. At finite coupling the mean field equations show a weak coupling solution that resembles the perturbative diagrams and a…

We discuss a D-dimensional Euclidean scalar field interacting with a scale invariant quantized metric. We assume that the metric depends on d-dimensional coordinates where d<D. We show that the interacting quantum fields have more regular…

Conformal self-dual fields in flat space-time of even dimension greater than or equal to four are studied. Ordinary-derivative formulation of such fields is developed. Gauge invariant Lagrangian with conventional kinetic terms and…

3D Gaussian Splatting (3DGS) has attracted great attention in novel view synthesis because of its superior rendering efficiency and high fidelity. However, the trained Gaussians suffer from severe zooming degradation due to non-adjustable…

We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale…

Applying the time-dependent variational principle of Balian and V\'en\'eroni, we derive variational approximations for multi-time correlation functions in $\Phi^4$ field theory. We assume first that the initial state is given and…