Related papers: Summing tree graphs at threshold
A method of reducing the problem of the calculation of tree multiparticle cross sections in $\phi^4$ theory to the solution of a singular classical Euclidean boundary value problem is introduced. The solutions are obtained numerically in…
A generating function is derived that counts the number of diagrams in an arbitrary scalar field theory. The number of graphs containing any number $n_j$ of $j$-point vertices is given. The count is also used to obtain the number of…
Following an argument advanced by Feynman, we consider a method for obtaining the effective action which generates the sum of tree diagrams with external physical particles. This technique is applied, in the unbroken \lambda \phi^4 theory,…
It is shown that the technique recently suggested by Lowell Brown for summing the tree graphs at threshold can be extended to calculate the loop effects. Explicit result is derived for the sum of one-loop graphs for the amplitude of…
Tree amplitudes of the production of two kinds of scalar particles at threshold from one virtual particle are calculated in a model of two scalar fields with $O(2)$ symmetric quartic interaction and unequal masses. These amplitudes exhibit…
The Euclidean quantum amplitude to go between data specified on an initial and a final hypersurface may be approximated by the tree amplitude exp(-I_{classical}/\hbar), where I_{classical} is the Euclidean action of the classical solution…
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 consider the problem of finding a subgraph of a given graph which minimizes the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already when all functions are the same, we show that it…
The method suggested by Lowell Brown for calculating multi-particle threshold amplitudes is extended to the one-loop level in scalar theories with broken reflection symmetry. A result for the threshold amplitude for multiparticle production…
Gauge theory amplitudes in a non-helicity format are generated at all $n$-point and at tree level. These amplitudes inherit structure from $\phi^3$ classical scattering, and the string inspired formalism is used to find the tensor algebra.…
We solve the classical euclidean boundary value problem for tree-level multiparticle production in $\phi^4$ theory at arbitrary energies in the case of $O(4)$ symmetric field configurations. We reproduce known low-energy results and obtain…
A shelling of a graph, viewed as an abstract simplicial complex that is pure of dimension 1, is an ordering of its edges such that every edge is adjacent to some other edges appeared previously. In this paper, we focus on complete bipartite…
We give an explicit formula for all tree amplitudes in N=4 SYM, derived by solving the recently presented supersymmetric tree-level recursion relations. The result is given in a compact, manifestly supersymmetric form and we show how to…
We apply the matrix-tree theorem to establish a link between various diagrammatic and determinant expressions, which naturally appear in scattering amplitudes of gravity theories. Using this link we are able to give a general…
Amplitudes $A_n$ in $d$-dimensional scalar field theory are generated, to all orders in the coupling constant and at $n$-point. The amplitudes are expressed as a series in the mass $m$ and coupling $\lambda$. The inputs are the classical…
The $k$-subset sum problem over finite fields is a classical NP-complete problem.Motivated by coding theory applications, a more complex problem is the higher $m$-th moment $k$-subset sum problem over finite fields. We show that there is a…
Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the matrix-tree theorem for the root system $D_n$ (the classical…
We give a proof for sharp estimate for the number of spanning trees using linear algebra and generalize this bound to multigraphs. In addition, we show that this bound is tight for complete graphs. In addition, we give estimates for number…
The Ward identities for amplitudes at the tree level are derived from symmetries of the corresponding classical dynamical systems. The results are applied to some 2 into n amplitudes.
We give exact formulas for the transmission (i.e. the sum of all distances between vertices) of perfect trees and rooted powers of (connected finite) graphs.