Related papers: Towards a categorification of scattering amplitude…
We develop a general theory of cluster categories, applying to a 2-Calabi-Yau extriangulated category $\mathcal{C}$ and cluster-tilting subcategory $\mathcal{T}$ satisfying only mild finiteness conditions. We show that the structure theory…
We introduce a new, probability-level approach to calculations in scalar field particle scattering. The approach involves the implicit summation over final states, which makes causality manifest since retarded propagators emerge naturally.…
Scattering diagrams arose in the context of mirror symmetry, Donaldson-Thomas theory, and integrable systems. We show that a consistent scattering diagram with minimal support cuts the ambient space into a complete fan. A special class of…
We present the amplitude for classical scattering of gravitationally interacting massive scalars at third post-Minkowskian order. Our approach harnesses powerful tools from the modern amplitudes program such as generalized unitarity and the…
Over the past two years, the use of on-shell techniques has deepened our understanding of the S-matrix of gauge theories and led to the calculation of many new scattering amplitudes. In these notes we review a particular on-shell method…
We present and numerically implement a computational method to construct relativistic scattering amplitudes that obey analyticity, crossing, elastic and inelastic unitarity in three and four spacetime dimensions. The algorithm is based on…
We consider several classes of analytic parametrisations of hadronic scattering amplitudes, and compare their predictions to all available forward data (p p, pbar p, pi p, K p, gamma p, gamma gamma, Sigma p). Although these parametrisations…
In the theory of triangulated categories, we propose to replace hearts of $t$-structures by proper abelian subcategories, which may be plentiful even when hearts are not. For instance, this happens in negative cluster categories. In support…
Very recently planar collections of Feynman diagrams were proposed by Borges and one of the authors as the natural generalization of Feynman diagrams for the computation of $k=3$ biadjoint amplitudes. Planar collections are one-dimensional…
The effective action includes all quantum corrections arising in a given quantum field theory. Thus it serves as a powerful generating functional from which quantum-corrected scattering amplitudes can be constructed via tree-level…
The theory of renormalized energy spectrum of a multi-level quasiparticle interacting with polarization phonons at $T=0$ K is developed within the Feynman-Pines diagram technique in a new approach. It permits a successive separation of…
Classification of cluster variables in cluster algebras (in particular, Grassmannian cluster algebras) is an important problem, which has direct application to computations of scattering amplitudes in physics. In this paper, we apply the…
There is a number of indications that scattering amplitudes in the Aharony-Bergman-Jafferis-Maldacena theory might have a dual description in terms of a holonomy of a supergauge connection on a null polygonal contour in a way analogous to…
We evaluate, in the high-energy limit, $s\gg|t|\gg m^2\gg\lambda^2$, the sum of amplitudes corresponding to a class of Feynman diagrams describing two-loop virtual photonic corrections to Bhabha scattering. The diagrams considered are box…
The purpose of this review is to bridge the gap between a standard course in quantum field theory and recent fascinating developments in the studies of on-shell scattering amplitudes. We build up the subject from basic quantum field theory,…
We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of `extended quivers' which are oriented hypergraphs. We describe mutations of such…
Feynman amplitudes in perturbation theory form the basis for most predictions in particle collider experiments. The mathematical quantities which occur as amplitudes include values of the Riemann zeta function and relate to fundamental…
We introduce the notion of a lower bound cluster algebra generated by projective cluster variables as a polynomial ring over the initial cluster variables and the so-called projective cluster variables. We show that under an acyclicity…
We consider the recently discovered, one parameter family of exactly solvable shape invariant potentials which are isospectral to the generalized P\"oschl-Teller potential. By explicitly considering the asymptotic behaviour of the Xm Jacobi…
We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in an unspecified covariant gauge. The complete Mellin representation of such amplitudes is…