Related papers: A New Approach for Analytic Amplitude Calculations
Using the newly modified method developed for symbolic evaluation of Feynman amplitudes we examine two processes $2\to 2$ (including a case of Majorana fermions) at a tree level. Constructing special polarization basis for spinor particles,…
A new method of calculation of amplitudes of different processes in quantum electrodynamics is proposed. The method does not use the Feynman technique of trace of product of matrices calculation. The method strongly simplifies calculation…
In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast…
We present a method for symbolic evaluation of Feynman amplitudes. We construct special polarization basis for spinor particles which produces compact expressions for tensor products of basis spinors.
We present a Mathematica package AmpRed for the semi-automatic calculations of multi-loop Feynman amplitudes with high efficiency and precision. AmpRed implements the methods of integration by parts and differential equations in the…
A method is developed whereby spinor helicity techniques can be used to simplify the calculation of loop amplitudes. This is achieved by using the Feynman-parameter representation where the offending off-shell loop momenta do not appear.…
We present an alternative approach for calculating helicity amplitudes for processes involving both massless and massive fermions. With this method one can easily obtain covariant expressions for the helicity amplitudes. The final…
A new approach for tree-level amplitudes with multiple fermion lines is presented. It mainly focuses on the simplification of fermion lines. By calculating two vectors recursively without any matrix multiplications, the result of a fermion…
Given a Feynman parameter integral, depending on a single discrete variable $N$ and a real parameter $\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in $\epsilon$. In a…
We device a new method to calculate a large number of Mellin moments of single scale quantities using the systems of differential and/or difference equations obtained by integration-by-parts identities between the corresponding Feynman…
Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R.…
Manifestly Lorentz covariant Feynman rules are given in terms of a "scalar" field for each helicity, dramatically simplifying the calculation of amplitudes with massless particles. The spinor helicity formalism is properly identified as a…
A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary…
We present a new variant of the spinor techniques for calculating the amplitudes of processes involving massive fermions with arbitrary polarization. It is relatively simple and leads to basic spinor products. Our procedure is not more…
We introduce a novel approach to compute Compton amplitudes involving a fermion pair inspired by Hopf algebra amplitude constructions. This approach features a recursive relation employing quasi-shuffle sets, directly verifiable by massive…
The paper presents the new method of calculations of reaction amplitudes of processes with spin 1/2 fermions. The method is based on the application of isotropic tetrad in Minkowski space and basis spinors connected with it. We obtained as…
Recently, we proposed a new approach for calculating Feynman graphs amplitude using the Gaussian representation for propagators which was proven to be exact in the limit of graphs having an infinite number of loops. Regge behavior was also…
We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…
We re express the fermion's probability amplitude as a trace over spinor indices, which formulation surprisingly does not exist in literature. This formulation puts the probabilty amplitude and the the probabilty(squared amplitude) of a…
In a recent paper \cite{ft} a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original…