Related papers: Angular integrals with three denominators via IBP,…
We study multi-propagator angular integrals, a class of phase-space integrals relevant to processes with multiple observed final states and a test-bed for transferring loop-integral technology to phase space integrals without reversed…
We compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric…
We discuss the evaluation of certain d dimensional angular integrals which arise in perturbative field theory calculations. We find that the angular integral with n denominators can be computed in terms of a certain special function, the…
We compute four-denominator angular phase-space integrals using the Mellin--Barnes (MB) technique in dimensional regularisation. Independent of the scattering process, an angular integral can be categorised based on the nature of the…
This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results…
We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of…
Non-integer dimensions are commonplace in quantum field theories (QFTs) through dimensional regularization. In particular this affects angular calculations involving dot products. The structure of these rises from the generally accepted…
Recent models for discrete euclidean quantum gravity incorporate a sum over simplicial triangulations. We describe an algorithm for simulating such models in general dimensions. As illustration we show results from simulations in four…
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…
The numerical simulation of three-dimensional charged-particle dynamics (CPD) under strong magnetic field is a basic and challenging algorithmic task in plasma physics. In this paper, we introduce a new methodology to design two-scale…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
We conduct numerical simulations of a model of four dimensional quantum gravity in which the path integral over continuum Euclidean metrics is approximated by a sum over combinatorial triangulations. At fixed volume the model contains a…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\text{\reflectbox{\text{p}}}\mkern-3mu\text{p}\left(q,p\right)$ which might be computed from the position-space wave function…
The isotropic 3-dimensional harmonic oscillator potential can serve as an approximate description of many systems in atomic, solid state, nuclear, and particle physics. In particular, the question of 2 particles binding (or coalescing) into…
Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of…
We discuss correspondence between the predictions of quantum theories for rotation angle formulated in infinite and finite dimensional Hilbert spaces, taking as example, the calculation of matrix elements of phase-angular momentum…
Recursion relations for integrals of amplitudes over the phase space, i.e. for partial wave amplitudes, are introduced. In their simplest form these integrals are proportional to the s-wave amplitudes and represent rigorous lower bounds on…
This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $\alpha$, and $\nu$. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicit analytic…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…