相关论文: Conformal invariance in two-dimensional percolatio…

In this review article, we discuss the distinction and possible equivalence between scale invariance and conformal invariance in relativistic quantum field theories. Under some technical assumptions, we can prove that scale invariant…

A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this…

We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…

A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…

The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are…

We study the critical behavior of various geometrical and transport properties of percolation in 6 dimensions. By employing field theory and renormalization group methods we analyze fluctuation induced logarithmic corrections to scaling up…

We propose that at the beginning of the universe gravity existed in a limbo either because it was switched off or because it was only conformally coupled to all particles. This picture can be reverse-engineered from the requirement that the…

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…

Percolation models describe the inside of a porous material. The theory emerged timidly in the middle of the twentieth century before becoming one of the major objects of interest in probability and mathematical physics. The golden age of…

We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle…

We investigate a one dimensional quantum mechanical model, which is invariant under translations and dilations but does not respect the conventional conformal invariance. We describe the possibility of modifying the conventional conformal…

We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic…

In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…

A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…

The main intention of the paper is to investigate an osculating curve under the conformal map. We obtain a sufficient condition for the conformal invariance of an osculating curve. We also find an equivalent system of a geodesic curve under…

We investigate a conformal invariant gravitational model which is taken to hold at pre-inflationary era. The conformal invariance allows to make a dynamical distinction between the two unit systems (or conformal frames) usually used in…

There has been a trend in the past decade to describe the large-scale structures in the Universe as a (multi)fractal set. However, one of the main objections raised by the opponents of this approach deals with the transition to homogeneity.…

The aim of this article is to give a rather extensive, and yet nontechnical, account of the birth of the regularity theory for generalized minimal surfaces, of its various ramifications along the decades, of the most recent developments,…

INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…

We give a short, critical review of the issue of decoherence. We establish the most general framework in which decoherence can be discussed, how it can be quantified and how it can be measured. We focus on environment induced decoherence…