相关论文: Knots, Feynman Diagrams and Matrix Models

A generalized canonical formulation of the theory of the electromagnetic Fokker interaction for a system of two particles is proposed. The functional integral on the generalized phase space is defined as the initial one in quantum theory.…

The authors studied in [Ann. Inst. Henri Poincar\'e D 9, 367-433, (2022)], a complex multi-matrix model with $\mathrm{U}(N)^2 \times \mathrm{O}(D)$ symmetry, and whose double scaling limit where simultaneously the large-$N$ and large-$D$…

We derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…

We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include…

We present a diagrammatic technique for calculating the free energy of the Hermitian one-matrix model to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint…

In the context of spin foam models for quantum gravity, group field theories are a useful tool allowing on the one hand a non-perturbative formulation of the partition function and on the other hand admitting an interpretation as…

Using the Feynman path integral representation of quantum mechanics it is possible to derive a model of an electron in a random system containing dense and weakly-coupled scatterers, see [Proc. Phys. Soc. 83, 495-496 (1964)]. The main goal…

We find that the overall UV divergences of a renormalizable field theory with trivalent vertices fulfil a four-term relation. They thus come close to establish a weight system. This provides a first explanation of the recent successful…

We extend the QCD Parton Model analysis by employing a factorized nuclear structure model that explicitly accounts for both individual nucleons and correlated nucleon pairs. This novel framework establishes a paradigm that directly links…

We study the free energy of an integrable, planar, chiral and non-unitary four-dimensional Yukawa theory, the bi-fermion fishnet theory discovered by Pittelli and Preti. The typical Feynman-diagrams of this model are of regular…

A seminal technique of theoretical physics called Wick's theorem interprets the Gaussian matrix integral of the products of the trace of powers of Hermitian matrices as the number of labelled maps with a given degree sequence, sorted by…

Let $D$ be a knot diagram, and let ${\mathcal D}$ denote the set of diagrams that can be obtained from $D$ by crossing exchanges. If $D$ has $n$ crossings, then ${\mathcal D}$ consists of $2^n$ diagrams. A folklore argument shows that at…

The Feynman-Hellmann theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing…

The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map.…

We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…

We review some relations occurring between the combinatorial intersection theory on the moduli spaces of stable curves and the asymptotic behavior of the 't Hooft-Kontsevich matrix integrals. In particular, we give an alternative proof of…

Fox coloring provides a combinatorial framework for studying dihedral representations of the knot group. The less well-known concept of Dehn coloring captures the same data. Recent work of Carter-Silver-Williams clarifies the relationship…

We describe an algorithm that recognizes some (perhaps all) intrinsically knotted (IK) graphs, and can help find knotless embeddings for graphs that are not IK. The algorithm, implemented as a Mathematica program, has already been used by…

We consider properties of connected diagrams with fermion-photon interaction and such fermion and photon propagators and vertex function that the values of these diagrams are finite. We establish the properties of these propagators and…

The topological string interpretation of homological knot invariants has led to several insights into the structure of the theory in the case of sl(N). We study possible extensions of the matrix factorization approach to knot homology for…