Related papers: Anomalous Threshold as the Pivot of Feynman Amplit…
These lectures on anomalies are relatively self-contained and intended for graduate students who are familiar with the basics of quantum field theory. We begin with several derivations of the abelian anomaly: anomalous transformation of the…
This review paper discusses the identification of regions, a crucial first step in applying the "method-of-regions" technique. A systematic approach based on Newton polytope geometry has proven successful and efficient for many cases.…
We discuss the threshold tree amplitudes in diverse nonintegrable quantum field theories in the framework of integrability. The amplitudes are related to some Baker functions defined on the auxiliary spectral curves and the nullification…
Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p-norm are established. Applications related to the celebrated Landau inequality between the norms of the…
We revisit the conjectural method called Schubert analysis for generating the alphabet of symbol letters for Feynman integrals, which was based on geometries of intersecting lines associated with corresponding cut diagrams. We explain the…
A two-layer system coupled via tunneling and with different carrier masses in each layer is investigated in the integer quantum Hall regime. Striking deviations of the one-layer Hall conductivity from the usual quantization are found, if…
We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in an unspecified covariant gauge. The complete Mellin representation of such amplitudes is…
In this article, we explore the structure of IR singularity of Feynman diagrams at one loop via power counting in loop momentum. The emphasis is on many known results which follow from this simple analysis.
We work with the Friedrichs extension of a one dimensional Schrodinger whose potential has a certain type of regular singularity near one end point. We study the effect on the eigenvalues of shrinking the region slightly near the end point.…
This article describes the \emph{Macaulay2} package \emph{FrobeniusThresholds}, designed to estimate and calculate $F$-pure thresholds, more general $F$-thresholds, and related numerical invariants arising in the study of singularities in…
I review some recent work on the problem of multiparticle production in a phi^4-theory with an O(N) symmetry. Threshold amplitudes with fixed number of produced particles are exactly calculated at large-N to all loops and vanish on mass…
Grating spectra exhibit sharp variations of the scattered light, known as grating anomalies. The latter are due to resonances that have fascinated specialists of optics and physics for decades and are nowadays used in many applications. We…
Because the chiral-odd structure function h_1 will be measured in the polarized Drell-Yan process, it is important to predict the behavior of h_1 before the measurement. In order to study the Q^2 evolution of h_1, we discuss one and two…
This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.
We show that to n loop order the divergent content of a Feynman amplitude is spanned by a set of basic (logarithmically divergent) integrals which need not be evaluated. Only the coefficients of the basic divergent integrals are necessary…
We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…
The evaluation of loop amplitudes via differential equations and harmonic polylogarithms is discussed at an introductory level. The method is based on evolution equations in the masses or in the external kinematical invariants and on a…
Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.
We discuss the origin of the Wilson polygon - MHV amplitude duality at the perturbative level. It is shown that the duality for the MHV amplitudes at one-loop level can be proven upon the peculiar change of variables in Feynman…
The method of expansion of integrals in external parameters is suggested. It is quite universal and works for Feynman integrals both in Euclidean and Minkowski regions of momenta.