Related papers: Four Lectures on Euler Integrals
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential…
We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric techniques. For very affine hypersurfaces, we investigate…
Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of…
We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space IBP relations, which are well-known in the physics literature. Applying a result of…
Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of…
We study several variants of Euler sums by using the methods of contour integration and residue theorem. These variants exhibit nice properties such as closed forms, reduction, etc., like classical Euler sums. In addition, we also define a…
The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it…
It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.
This monograph discusses dualities in physics: what dualities are, their main examples--from quantum mechanics and electrodynamics to statistical mechanics, quantum field theory and string theory--and the philosophical questions they raise.…
We provide a new method to calculate the full microlocal description of singularities of Feynman integrals. This is done by associating a unique constructible function to the system of partial differential equations (PDEs) annihilating the…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
Feynman diagrams are a pictorial way of describing integrals predicting possible outcomes of interactions of subatomic particles in the context of quantum field physics. It is highly desirable to have an intrinsic mathematical…
We present linear forms with integer coefficients containing the Euler-Mascheroni and Euler-Gompertz constants. The forms are defined by four-terms recurrence relations. Asymptotics of the forms and their coefficients are obtained.
A general procedure for the calculation of a class of two-loop Feynman diagrams is described. These are two-point functions containing three massive propagators, raised to integer powers, in the denominator, and arbitrary polynomials of the…
The phenomenological aspects of string theory are briefly reviewed. Emphasis is given to the status of 4D string model building, effective Lagrangians, model independent results, supersymmetry breaking and duality symmetries.
Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…
We consider a nonlinear generalization of Cauchy-Riemann eqs. to the algebra of biquaternions. From here we come to "universal generating equations" (1) which deal with 2-spinor and gauge fields and form the basis of some unified algebraic…
The Euler numbers have been widely studied. A signed version of the Euler numbers of even subscript are given by the coefficients of the exponential generating function 1/(1+x^2/2!+x^4/4!+...). Leeming and MacLeod introduced a…
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of…
These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, using quaternions and Clifford algebras in higher dimensions. The main themes are weak solutions, the mean-value property, and subharmonicity.