Related papers: Position Space Equations for Banana Feynman Diagra…
In quantum field theory with three-point and four-point couplings the Feynman diagrams of perturbation theory contain momentum independent subdiagrams, the ``tadpoles'' and ``snails''. With the help of Dyson-Schwinger equations we show how…
This note is devoted to representation of some evolution semigroups. The semigroups are generated by pseudo-differential operators, which are obtained by different (parametrized by a number $\tau$) procedures of quantization from a certain…
Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and…
The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is…
We describe the "Feynman diagram" approach to nonrelativistic quantum mechanics on R^n, with magnetic and potential terms. In particular, for each classical path \gamma connecting points q_0 and q_1 in time t, we define a formal power…
We compute the two and three loop corrections to the beta function for Yang-Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one…
In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N=4 SYM theory. In this letter we show that integrability also features in the building blocks of massive…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
Higher-order diagrams required for radiative corrections to mixed electroweak and QCD processes at the LHC and anticipated future colliders will require numerically stable representations of the associated Feynman diagrams. The…
We perform a comprehensive study of a certain class of discrete symmetries of families of Feynman integrals, defined as affine changes of variables that map different sectors of the family into each other. We show that these transformations…
In the semiclassical approximation in which the electric charges of scalar particles are described by Grassmann variables ($Q_i^2=0, Q_iQ_j\ne 0$), it is possible to re-express the Lienard-Wiechert potentials and electric fields in the…
We show that direct Feynman-parametric loop integration is possible for a large class of planar multi-loop integrals. Much of this follows from the existence of manifestly dual-conformal Feynman-parametric representations of planar loop…
We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…
Following the thread of R. Gastmans, S. L. Wu and T. T. Wu, the calculation in the unitary gauge for the $H \to \gamma \gamma$ process via one W loop is repeated, but without the specific choice of the independent loop momentum for the…
In this paper we consider systems of quantum particles in the $4d$ Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the…
We find empirically that the value of Feynman integrals follows a $\log$-$\Gamma$ distribution at large loop order. This result opens up a new avenue towards the large-order behavior in perturbative quantum field theory. Our study of the…
Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. We provide a…
It is shown that the usual expression for a Feynman diagram in terms of the Feynman propagator $\Delta_F(x-y)$ can be replaced by an equivalent expression involving the positive-energy on-shell propagator $\Delta^+(x-y)$, supplemented by…
We verify a method which allows to obtain the $\beta$-function of supersymmetric theories regularized by higher covariant derivatives by calculating only specially modified vacuum supergraphs. With the help of this method for a general…
In this paper DeWitt's formalism for field theories is presented; it provides a framework in which the quantization of fields possessing infinite dimensional invariance groups may be carried out in a manifestly covariant (non-Hamiltonian)…