相关论文: Difference Equations and Integral Families for Wit…

Conformally invariant wave equations in de Sitter space, for scalar and vector fields, are introduced in the present paper. Solutions of their wave equations and the related two-point functions, in the ambient space notation, have been…

We show how a large class of Feynman integrals can be efficiently reduced to master integrals by suitable covariant differentiation on the vector space dual to the one spanned by the master integrals. The connections needed in the covariant…

We point out that an infinite class of Witten diagrams is invariant under a Yangian symmetry. These diagrams are building blocks of holographic correlators and are related by a web of differential recursion relations. We show that Yangian…

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…

The calculation of loop corrections to the correlation functions of quantum fields during inflation or in the de~Sitter background presents greater challenges than in flat space due to the more complicated form of the mode functions. While…

We compute all planar two-loop six-point Feynman integrals entering scattering observables in massless gauge theories such as QCD. A central result of this paper is the formulation of the differential-equations method under the algebraic…

In this article we give new examples of models in boundary quantum field theory, i.e. local time-translation covariant nets of von Neumann algebras, using a recent construction of Longo and Witten, which uses a local conformal net A on the…

We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent…

Witten diagrams are basic objects for studying dynamics in AdS space, and also play key roles in the analytic functional bootstrap. However, these diagrams are notoriously hard to evaluate, making it extremely difficult to search for…

Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension $d$ in terms of (generalized) hypergeometric functions $_2F_1$ and $F_1$. Values at asymptotic or…

A new type of integral representation is proposed for the propagators of the massive Klein-Gordon field minimally coupled to the gravity of the de Sitter expanding universe. This representation encapsulates the effects of the Heaviside step…

We explore two-point and four-point correlation functions of a massive scalar field on the flat de Sitter background in the long-wavelength approximation. By employing the Yang-Feldman-type equation, we compute the two-point correlation…

Infrared divergences in Quantum Field Theory govern the low-energy dynamics of many physical theories, and their understanding is a crucial ingredient in predicting the outcomes of collider experiments. We present a novel approach to…

Some general remarks are made about the quantum theory of scalar fields and the definition of momentum in curved space. Special emphasis is given to field theory in anti-de Sitter space, as it represents a maximally symmetric space-time of…

Recent developments in quantum chemistry, perturbative quantum field theory, statistical physics or stochastic differential equations require the introduction of new families of Feynman-type diagrams. These new families arise in various…

We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered…

We argue that generic one-loop scattering amplitudes in supersymmetric Yang-Mills theories can be computed equivalently with MHV diagrams or with Feynman diagrams. We first present a general proof of the covariance of one-loop non-MHV…

The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension $d$ has been solved for the basis of scalar one- to four-point functions with indices one. In 2003…

The quantum fluctuations of a test scalar field on superhorizon scale in de Sitter spacetime can be described by an effective one-dimensional stochastic theory corresponding to a particular class of nonequilibrium dynamical systems known as…

A spacetime interpretation of deformed relativity symmetry groups was recently proposed by resorting to Finslerian geometries, seen as the outcome of a continuous limit endowed with first order corrections from the quantum gravity regime.…