Related papers: Renormalization Theory in the Electrostatic and Ve…
We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of [SS1,SS3]. Roughly speaking, it is obtained…
Through introducing a notion of renormalization of particle-number density, a simple perturbation scheme of nonequilibrium quantum-field theory is proposed. In terms of the renormalized particle-distribution functions, which characterize…
We obtain the two-loop effective potential for general renormalizable theories, using a generalized gauge-fixing scheme that includes as special cases the background-field $R_\xi$ gauges, the Fermi gauges, and the familiar Landau gauge, and…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…
We study the P\"oschl-Teller potential $V(x) = \alpha^2 g_s \sinh^{-2}(\alpha x) + \alpha^2 g_c \cosh^{-2}(\alpha x)$, for every value of the dimensionless parameters $g_s$ and $g_c$, including the less usual ranges for which the regular…
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…
We discuss the peculiar features of the renormalization procedure in the case of infinite-component effective theory. It is shown that in the case of physically interesting theories (namely, those leading to the amplitudes with asymptotic…
We study two--loop renormalization in $(2+\epsilon)$--dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the…
We consider all radiative corrections to the total electron-positron cross section showing how the renormalization group equation can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log etc.…
We study the radial Schr\"odinger equation for a particle of mass $m$ in the field of a singular attractive $g^2/{r^4}$ potential with particular emphasis on the bound states problem. Using the regularization method of Beane \textit{et…
We examine whether renormalization effects can cause Newton's constant to change dramatically with energy, perhaps even reducing the scale of quantum gravity to the TeV region without the introduction of extra dimensions. We examine a model…
Despite the success of quantum field theories, the origin of the mass of elementary particles persists. The renormalization program is an essential part of the calculation of the scattering amplitudes, where the infinities of the calculated…
The algebraic method of renormalization is applied to the standard model of electroweak interactions. We present the most important modifications compared to theories with simple groups.
This paper is devoted to the analysis of the divergence of the electron self-energy in classical electrodynamics. To do so, we appeal to the theory of distributions and a method for obtaining corresponding extensions. At first sight,…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon…
We outline a general formalism for treating vacuum polarization phenomena within an effective field expansion. The coupling between source charges and virtual fields is examined from the perspectives of electrostatic potentials, induced…
The problem of an enormously large energy density of the quantum vacuum is discussed in connection with the concept of renormalization of physical parameters in quantum field theory. Using the method of dimensional regularization, it is…
A field theoretic renormalization group method is presented which is capable of dealing with crossover problems associated with a change in the upper critical dimension. The method leads to flow functions for the parameters and coupling…
We present a new method to renormalize stochastic differential equations subjected to multiplicative noise. The method is based on the widely used concept of effective potential in high energy physics, and has already been successfully…