Related papers: The chirality-flow formalism
In a recent paper we introduced the chirality-flow formalism, a method for simple and transparent calculations of Feynman diagrams based on the left- and right-chiral $\mathrm{sl}(2,\mathbb{C})$ nature of spacetime. While our previous work…
Inspired by the flow description of su(N) colour calculations, we recently showed how to simplify the spinor-helicity formalism (at the algebra level two copies of complexified su(2)) by treating each Weyl spinor as part of a flow line with…
In a few recent papers we introduced the chirality-flow formalism, which was shown to make calculations of tree-level Feynman diagrams simple and transparent. Chirality flow, which is based on the spinor-helicity formalism, allows to often…
Scattering amplitudes are often split up into their color (su(N)) and kinematic components. Since the su(N) gauge part can be described using flows of color, one may anticipate that the double su(2) kinematic part can be described in terms…
Recently we introduced the chirality-flow formalism, a method which builds on the spinor-helicity formalism and is inspired by the color-flow idea in QCD. With this formalism, Feynman rules and diagrams are simplified to the extent that it…
The chirality-flow formalism, combined with good choices of gauge reference vectors, simplifies tree-level calculations to the extent that it is often possible to write down amplitudes corresponding to Feynman diagrams immediately. It has…
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 propose a new helicity formalism based on the formal insertion in spinor lines of a complete set of states build up with unphysical spinors. The method is developed both for massless and massive fermions for which it turns out to be…
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…
The bilinear combination of Dirac spinors $u(p_1,n_1)\bar u(p_2,n_2)$ is expressed in terms of Lorentz vectors in an explicit covariant form. The fact that the obtained expression involves only one auxiliary vector makes it very convenient…
A way to efficiently compute helicity amplitudes for arbitrary tree-level scattering processes in QCD is presented. The scattering amplitude is evaluated recursively through a set of Dyson-Schwinger equations. The computational cost of this…
We present a general formalism for simplifying manipulations of spin indices of massless and massive spinors and vectors in Feynman diagrams. The formalism is based on covariantly reducing the number of field components in the action in…
The gradient-flow formalism is applied to a non-Abelian gauge theory with scalar and fermionic particles, dubbed "scalar QCD". It is shown that the flowed scalar quark requires a field renormalization, albeit only beyond the one-loop level.…
The worldline formalism shares with string theory the property that it allows one to write down master integrals that effectively combine the contributions of many Feynman diagrams. While at the one-loop level these diagrams differ only by…
Simultaneously with inventing the modern relativistic formalism of quantum electrodynamics, Feynman presented also a first-quantized representation of QED in terms of worldline path integrals. Although this alternative formulation has been…
We summarize recent progress in applying the worldline formalism to the analytic calculation of one-loop N-point amplitudes. This string-inspired approach is well-adapted to avoiding some of the calculational inefficiencies of the standard…
We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional…
We use the worldline path-integral approach to the Bern-Kosower formalism for developing a new algorithm for calculation of the sum of all diagrams with one spinor loop and fixed numbers of external and internal photons. The method is based…
In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…
We discuss the enumeration of Feynman diagrams at tree order for processes with external lines of different types. We show how this can be done by iterating algebraic Schwinger-Dyson equations. Asymptotic estimates for very many external…