相关论文: Factorization of Spanning Trees on Feynman Graphs
Recently, we proposed a new approach for calculating Feynman graphs amplitude using the Gaussian representation for propagators which was proven to be exact in the limit of graphs having an infinite number of loops. Regge behavior was also…
The propagator of a virtual $\phi$-field with emission of $n$ on-mass-shell particles all being exactly at rest is calculated at the tree-level in $\lambda \phi^4$ theory by directly solving recursion equations for the sum of Feynman…
Feynman diagrams are the foremost tool in the perturbative study of quantum field theory. In gauge theories, the full potential of this tool is revealed when it is combined with the Slavanov-Taylor identities associated with the local gauge…
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…
Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates. Here we restrict to planar trees since each…
It was proposed in hep-th/0403047 that all tree amplitudes in pure Yang-Mills theory can be constructed from known MHV amplitudes. We apply this approach for calculating tree amplitudes of gauge fields and fermions and find agreement with…
We prove a neat factorization property of Feynman graphs in covariant perturbation theory. The contribution of the graph to the effective action is written as a product of a massless scalar momentum integral that only depends on the basic…
We give combinatorial criteria for predicting the transcendental weight of Feynman integrals of certain graphs in $\phi^4$ theory. By studying spanning forest polynomials, we obtain operations on graphs which are weight-preserving, and a…
In the models defined on the inhomogeneous background the propagators depend on the two space - time momenta rather than on one momentum as in the homogeneous systems. Therefore, the conventional Feynman diagrams contain extra integrations…
A unified treatment of Schwinger parametrised Feynman amplitudes is suggested which addresses vertices of arbitrary order on the same footing as propagators. Contributions from distinct diagrams are organised collectively. The scheme is…
We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based…
We give factorizations for weighted spanning tree enumerators of Cartesian products of complete graphs, keeping track of fine weights related to degree sequences and edge directions. Our methods combine Kirchhoff's Matrix-Tree Theorem with…
An $\alpha$-parameter representation is derived for gauge field theories.It involves, relative to a scalar field theory, only constants and derivatives with respect to the $\alpha$-parameters. Simple rules are given to obtain the…
We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc function representation for the propagators of…
We examine a large class of scalar quantum field theories where vertices are able to cancel adjacent propagators. These theories are obtained as diffeomorphisms of the field variable of a free field. Their connected correlations functions…
The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees…
We generalize Gopakumar's microscopic derivation of Witten diagrams in large N free quantum field theory [1] to interacting theories in perturbative expansion. For simplicity we consider a matrix scalar field with $\Phi^h$ interaction in d…
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…
We derive a minimal set of Feynman rules for the loop amplitudes in unitary models of closed strings, whose target space is a simply laced (extended) Dynkin diagram. The string field Feynman graphs are composed of propagators, vertices…
We show that the series expansion of quantum field theory in the Feynman diagrams can be explicitly mapped on the partition function of the simplicial string theory -- the theory describing embeddings of the two--dimensional simplicial…