Related papers: Enumeration of N-rooted maps using quantum field t…
This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S-matrix, Feynman…
We investigate the relationship between the universal topological polynomials for graphs in mathematics and the parametric representation of Feynman amplitudes in quantum field theory. In this first paper we consider translation invariant…
For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph…
We present a surprisingly new connection between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorial maps on the other hand. We describe a bijection between these two…
The purpose of this paper is to study some properties of the Newton maps associated to real quintic polynomials. First using the Tschirnhaus transformation, we reduce the study of Newton's method for general quintic polynomials to the case…
This paper addresses the enumeration of rooted and unrooted hypermaps of a given genus. For rooted hypermaps the enumeration method consists of considering the more general family of multirooted hypermaps, in which darts other than the root…
We give closed form expressions for the numbers of multi-rooted plane trees with specified degrees of root vertices. This results in an infinite number of integer sequences some of which are known to have an alternative interpretation. We…
The main purpose is to characterise continuous maps that are $n$-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius $n$-homomorphisms between two function spaces that correspond to…
A well-known connection between n strings winding around a circle and permutations of n objects plays a fundamental role in the string theory of large N two dimensional Yang Mills theory and elsewhere in topological and physical string…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…
The paper considers the behaviour of the number of paths of length $N$ on graphs with two heavy roots. Such vertices can be entropic traps. Numerical analysis is carried out for graphs with different degrees of root vertices. In the…
The work that consists of two parts is devoted to the problem of enumerating unrooted $r$-regular maps on the torus up to all its symmetries. We begin with enumerating near-$r$-regular rooted maps on the torus, projective plane and the…
A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on…
Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT).…
We completely generalize previous results related to the counting of connected Feynman diagrams. We use a generating function approach, which encodes the Wick contraction combinatorics of the respective connected diagrams. Exact solutions…
The first application of a quantum algorithm to Feynman loop integrals is reviewed. The connection between quantum computing and perturbative quantum field theory is feasible due to fact that the two on-shell states of a Feynman propagator…
We present a simple technique that allows to generate Feynman diagrams for vector models with interactions of order $2n$ and similar models (Gross-Neveu, Thirring model), using a bootstrap equation that uses only the free field value of the…
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…
We present a method for a recursive graphical construction of Feynman diagrams with their correct multiplicities in quantum electrodynamics. The method is first applied to find all diagrams contributing to the vacuum energy from which all…
It is shown that graphs that generalize the ADE Dynkin diagrams and have appeared in various contexts of two-dimensional field theory may be regarded in a natural way as encoding the geometry of a root system. After recalling what are the…