Related papers: Tutorial on loop integrals which need regularisati…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.
We present a simple, new method for the 1-loop renormalization of integrable $\sigma$-models. By treating equations of motion and Bianchi identities on an equal footing, we derive 'universal' formulae for the 1-loop on-shell divergences,…
We give a number of constructions where inverse limits seriously degrade properties of regular rings, such as unit-regularity, diagonalisation of matrices, and finite stable rank. This raises the possibility of using inverse limits to…
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…
This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their…
We present a systematic study of integrals over [0,1] where the integrand is of the form Q(x) log log 1/x. Here Q is a rational function.
Radiative corrections to the $h\rightarrow Z\gamma$ are evaluated in the one-loop approximation. The unitary gauge gauge is used. The analytic result is expressed in terms of the Passarino-Veltman functions. The calculations are applicable…
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
Decay amplitude of $H \to \gamma Z$ process via one $W$ loop in the unitary gauge is presented. The divergent integrals including those of high divergence orders typical of unitary gauge are arranged to cancel to get the electromagnetic…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
In this work we compute the leading logarithmic corrections to the b -> s gamma decay in a dimensional scheme which does not require any definition of the gamma5 matrix. The scheme does not exhibit unconsistencies and it is therefore a…
An Introduction to Hopf algebras as a tool for the regularization of relavent quantities in quantum field theory is given. We deform algebraic spaces by introducing q as a regulator of a non-commutative and non-cocommutative Hopf algebra.…
Some quantum mechanical potentials, singular at short distances, lead to ultraviolet divergences when used in perturbation theory. Exactly as in quantum field theories, but much simpler, regularization and renormalization lead to finite…
A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is…
In this paper we answer positively a question of whether it is possible for a circle diffeomorphism with breaks to be smoothly conjugate to a rigid rotation in the case when its breaks are lying on pairwise distinct trajectories. An example…
Local bifurcation theory typically deals with the response of a degenerate but isolated equilibrium state or periodic orbit of a dynamical system to perturbations controlled by one or more independent parameters, and characteristically uses…
Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a computer program. A list of examples is provided.
These notes present a first graduate course in harmonic analysis. The first part emphasizes Fourier series, since so many aspects of harmonic analysis arise already in that classical context. The Hilbert transform is treated on the circle,…
Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial…