Related papers: Rectangular amplitudes, conformal blocks, and appl…
We compute the perturbative short-time expansion for the transition amplitude of a particle in curved space time, by employing Dimensional Regularization (DR) to treat the divergences which occur in some Feynman diagrams. The present work…
In this paper, we will make an attempt to clarify the relation between three-dimensional euclidean loop quantum gravity with vanishing cosmological constant and quantum field theory in the continuum. We will argue, in particular, that in…
Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…
In two-dimensional critical loop models, including the $O(n)$ and Potts models, the spectrum is exactly known, as are a few structure constants or ratios thereof. Using numerical conformal bootstrap methods, we study $235$ of the simplest…
Open effective field theories provide a systematic framework for describing physical systems interacting with an environment whose microscopic details are unknown, unobservable, or uncalculable. A basic step in constructing any effective…
A beam of rotating dipolar particles (molecules or clusters) will broaden when passed through an electric or magnetic field gradient region. This broadening, which is a common experimental observable, can be expressed in terms of the…
The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann…
Vertical-arrow fluctuations near the boundaries in the six-vertex model on the two-dimensional $N \times N$ square lattice with the domain wall boundary conditions are considered. The one-point correlation function (`boundary polarization')…
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to a…
Characteristic modes of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions. The presented closed-form formulas lead to a proposal of precise…
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We consider the coagulation-decoagulation model on an one-dimensional lattice of length $L$ with open boundary conditions. Based on the empty interval approach the time evolution is described by a system of $\frac{L(L+1)}{2}$ differential…
We study integrals appearing in one-loop amplitudes in string theory, and in particular their analytic continuation based on a string theoretic analog of the $i\varepsilon$-prescription of quantum field theory. For various zero- and…
We give sufficient conditions for the bounded law of the iterated logarithms for strictly stationary random fields when the summation is done on rectangle. The study is done by the control of an appropriated maximal function. The case of…
We review some recent developments in the understanding of field theories in the perturbative regime. In particular, we discuss the notions of analyticity, unitarity and locality, and therefore the singularity structure of scattering…
We introduce a 2-dimensional lattice model of granular matter. We use a combination of proof and simulation to demonstrate an order/disorder phase transition in the model, to which we associate the granular phenomenon of random close…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…