相关论文: Vacuum Integration: UV- and IR-divergencies

The effective potential is known to be given by the vacuum diagrams. In this paper we show that the massive loop integrations corresponding to the vacuum diagrams can be expressed through the massless loop integrations with the…

It is known that the same physical system can be described by different effective theories depending on the scale at which it is observed. In this work, we formulate a prescription for finding the unitary that best approximates the large…

A method is introduced to calculate the UV-divergent parts at one-loop level in dimensional regularization. The method is based on the recursion, and the basic integrals are just the scaleless integrals after the recursive reduction, which…

We study a non-commutative non-relativistic scalar field theory in 2+1 dimensions. The theory shows the UV/IR mixing typical of QFT on non-commutative spaces. The one-loop correction to the two-point function turns out to be given by a…

We compare the accuracy of various methods for determining the transfer of the diffuse Lyman continuum in HII regions, by comparing them with a high-resolution discrete-ordinate integration. We use these results to suggest how, in…

Mathematical justifications are given for several integral and series representations of the Dirac delta function which appear in the physics literature. These include integrals of products of Airy functions, and of Coulomb wave functions;…

We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral…

An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…

In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…

Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals…

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…

The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…

Range-separated density-functional theory is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into…

In the present paper we introduce a multi-dimensional version of the R-matrix approach to the construction of integrable hierarchies. Applying this method to the case of the Lie algebra of functions with respect to the contact bracket, we…

We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on , the scaling parameter separating the time scale of the slow…

This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…

In this paper we consider IR divergences in a 3d toy model field theory for 4d holographic cosmology, and we analyze them by introducing a mass term in a way that preserves a certain form of the generalized conformal structure. This allows…

Excluded-volume effects can play an important role in determining transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two or three dimensions is considered systematically…

We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…

Discrete delta functions define the limits of attainable spatial resolution for all imaging systems. Here we construct broad, multi-dimensional discrete functions that replicate closely the action of a Dirac delta function under aperiodic…