相关论文: Adelic Amplitudes and Intricacies of Infinite Prod…
On the basis of analysis on the adele ring of any algebraic numbers field (Tate's formula) a regularization for divergent adelic products of gamma- and beta-functions for all completions of this field are proposed, and corresponding…
Unconstrained partial-wave amplitudes obtained at discrete energies from fits to complete sets of eight independent observables which are required to uniquely reconstruct reaction amplitudes do not vary smoothly with energy, and are in…
We present the first numerical calculation of the 4D Euclidean spin foam vertex amplitude for vertices with hypercubic combinatorics. Concretely, we compute the amplitude for coherent boundary data peaked on cuboid and frustum shapes. We…
We study numerically the continuum limit corresponding to the non-trivial fixed point of Dyson's hierarchical model. We discuss the possibility of using the critical amplitudes as input parameters. We determine numerically the leading and…
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this…
The Veneziano amplitude was put forward as a solution to the axioms of the S-matrix bootstrap. However, unitarity, reflected in the positivity of the coefficients in the Gegenbauer expansion of the amplitude is not obvious. In this note we…
We regularize in a continuous manner the path integral of QED by construction of a non-local version of its action by means of a regularized form of Dirac's $\delta$ functions. Since the action and the measure are both invariant under the…
We investigate $2 \to 3$ QCD scattering amplitudes in multi-Regge kinematics, i.e. where the final partons are strongly ordered in rapidity. In this regime amplitudes exhibit intriguing factorisation properties which can be understood in…
Let $\underline{E}=\prod_{p\in\mathbb{P}}E_p$ be a compact subset of $\widehat{\mathbb{Z}}=\prod_{p\in\mathbb{P}}\mathbb{Z}_p$ and denote by $\mathcal C(\underline{E},\widehat{\mathbb{Z}})$ the ring of continuous functions from…
In this follow-up paper, we again inspect a surprising relationship between the set of $n$-periodic points of a polynomial map $\varphi_{d, c}$ defined by $\varphi_{d, c}(z) = z^d + c$ for all $c, z \in \mathbb{Z}_{p}$ or $\in…
At leading order in weak and electromagnetic couplings, cross sections for (anti)neutrino-nucleon elastic scattering are determined by four nucleon form factors that depend on the momentum transfer $Q^2$. Including radiative corrections in…
We consider the parametric representation of the amplitudes of Abelian models in the so-called framework of rank $d$ Tensorial Group Field Theory. These models are called Abelian because their fields live on $U(1)^D$. We concentrate on the…
We present a complete set of 4-point amplitudes in the constructive Standard Model at tree level. Any 4-point amplitude can be obtained from the results presented here by a suitable choice of masses, a permutation of the particles (by…
We use partial wave unitarity to constrain various bespoke four-point amplitudes. We start by constructing bespoke generalizations of the type I superstring amplitude, which we show satisfy dual resonance and have suitable high-energy…
Using the helicity-spinor language we explore the non-perturbative constraints that Lorentz symmetry imposes on three-point amplitudes where the asymptotic states can be massive. As it is well known, in the case of only massless states the…
In this paper, we will show that the $p$-adic valuation (where $p$ is a given prime number) of some type of rational numbers is unusually large. This generalizes the very recent results by the author and by A. Dubickas, which are both…
We examine several zero-range potentials in non-relativistic quantum mechanics. The study of such potentials requires regularization and renormalization. We contrast physical results obtained using dimensional regularization and cutoff…
New approach to computing the amplitudes of multi-particle processes in renormalizable quantum field theories is presented. Its major feature is a separation of the renormalization from the computation. Within the suggested approach new…
In this paper, for a geometrically integral projective scheme, we will give an upper bound of the product of the norms of its non-geometrically integral reductions over an arbitrary number field. For this aim, we take the adelic viewpoint…
A set of 13 linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle is derived which respect Lorentz and gauge invariance. The $T$-matrix can be represented by a…