Related papers: Quadratic Feynman Loop Integrands From Massless Sc…
In this paper, we study systematically scalar one-loop two-, three-, and four-point Feynman integrals with complex internal masses. Our analytic results presented in this report are valid for both real and complex internal masses. The…
A double-cover extension of the scattering equation formalism of Cachazo, He and Yuan (CHY) leads us to conjecture covariant factorization formulas of n-particle scattering amplitudes in Yang-Mills theories. Evidence is given that these…
We show that the problem of solving recurrence relations for L-loop (R+1)-point Feynman integrals within the method of integration by parts is equivalent to the corresponding problem for (L+R)-loop vacuum or (L+R-1)-loop propagator-type…
We evaluate the fermion propagator in parity-conserving QED_3 with N flavours, in the context of an IR domain approximation. This provides results which are non-perturbative in the loopwise expansion sense. We include fermion-loop effects,…
We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm allows us…
In this work we solve exactly a class of three-body propagators for the most general quadratic interactions in the coordinates, for arbitrary masses and couplings. This is done both for the constant as the time-dependent couplings and…
We present a review of the relations between various equations for maximal cut banana Feynman diagrams, i.e. amplitudes with propagators substituted with $\delta$-functions. We consider both equal and generic masses. There are three types…
We study the convergence in $L^2$ of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in Physics and Chemistry, the approximate propagators considered here…
In the context of high-energy particle physics, a reliable theory-experiment confrontation requires precise theoretical predictions. This translates into accessing higher-perturbative orders, and when we pursue this objective, we inevitably…
Recently there is an alternative reduction method proposed by Chen in [1,2]. In this paper, using the one-loop scalar integrals with propagators having higher power, we show the power of the improved version of Chen's new method in which we…
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 formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.
We develop an iterative method for constructing four-dimensional generalized unitarity cuts in $\mathcal{N} = 2$ supersymmetric Yang-Mills (SYM) theory coupled to fundamental matter hypermultiplets ($\mathcal{N} = 2$ SQCD). For iterated…
We give a brief overview of the Yangian symmetry of Feynman integrals. After a short introduction to the Yangian and integrability, we motivate the emergence of integrable structures for Feynman integrals via the fishnet limit of AdS/CFT.…
We consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this…
We propose that Feynman integral reduction is controlled by solutions of the Landau equations. We study integral relations with prescribed propagator powers using syzygy methods and discuss how syzygies can be expressed as a sum over…
Given any (Feynman) propagator which is Lorentz and translation invariant, it is possible to construct an action functional for a scalar field such that the quantum field theory, obtained by path integral quantization, leads to this…
In this letter we compute a canonical set of cuts of the integrand for MHV amplitudes in planar ${\cal N}=4$ SYM, where all internal propagators are put on-shell. These "deepest cuts" probe the most complicated Feynman diagrams and on-shell…
Feynman integrals with generic propagator powers in one and two spacetime dimensions are investigated from various perspectives. In particular, we argue that the class of track integrals at any loop order is fixed by the recently found…
We present an interesting study of Feynman integral reduction that does not employ integration-by-parts identities. Our approach proceeds by studying the equivalence relations of integral contours in the Feynman parameterization. We find…